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A study on some paranormed sequence spaces due to Lambda–Pascal matrix 由 Lambda-Pascal 矩阵引起的若干准矩阵序列空间研究
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-03-26 DOI: 10.1007/s44146-024-00124-y
Taja Yaying, Feyzi Başar
{"title":"A study on some paranormed sequence spaces due to Lambda–Pascal matrix","authors":"Taja Yaying,&nbsp;Feyzi Başar","doi":"10.1007/s44146-024-00124-y","DOIUrl":"10.1007/s44146-024-00124-y","url":null,"abstract":"<div><p>This paper delves into the examination of algebraic and topological attributes associated with the domains <span>(c_0(G,q))</span>, <i>c</i>(<i>G</i>, <i>q</i>), and <span>(ell _infty (G,q))</span> pertaining to the Lambda–Pascal matrix <i>G</i> in Maddox’s spaces <span>(c_0(q))</span>, <i>c</i>(<i>q</i>), and <span>(ell _infty (q))</span>, respectively. The determination of the Schauder basis and the computation of <span>(alpha )</span>-, <span>(beta )</span>-, and <span>(gamma )</span>-duals for these Lambda–Pascal paranormed spaces are carried out. The ultimate section is dedicated to elucidating the classification of the matrix classes <span>((ell _{infty }(G,q),ell _{infty }))</span>, <span>((ell _{infty }(G,q),f))</span>, and <span>((ell _{infty }(G,q),c))</span>, concurrently presenting the characterization of specific other sets of matrix transformations in the space <span>(ell _{infty }(G,q))</span> as corollaries derived from the primary outcomes.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"161 - 180"},"PeriodicalIF":0.5,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140379456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convex geometries representable with colors, by ellipses on the plane, and impossible by circles 用颜色、平面上的椭圆和不可能用圆表示的凸面几何图形
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-03-25 DOI: 10.1007/s44146-024-00112-2
Kira Adaricheva, Evan Daisy, Ayush Garg, Grace Ma, Michelle Olson, Cat Raanes, James Thompson
{"title":"Convex geometries representable with colors, by ellipses on the plane, and impossible by circles","authors":"Kira Adaricheva,&nbsp;Evan Daisy,&nbsp;Ayush Garg,&nbsp;Grace Ma,&nbsp;Michelle Olson,&nbsp;Cat Raanes,&nbsp;James Thompson","doi":"10.1007/s44146-024-00112-2","DOIUrl":"10.1007/s44146-024-00112-2","url":null,"abstract":"<div><p>A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat (Discrete Math 342(N3):726–746, 2019) and the Polymath REU 2020 team (Convex geometries representable by at most 5 circles on the plane. arXiv:2008.13077), continues to investigate representations of convex geometries on a 5-element base set. It introduces several properties: the opposite property, nested triangle property, area Q property, and separation property, of convex geometries of circles on a plane, preventing this representation for numerous convex geometries on a 5-element base set. It also demonstrates that all 672 convex geometries on a 5-element base set have a representation by ellipses, as given in the appendix for those without a known representation by circles, and introduces a method of expanding representation with circles by defining unary predicates, shown as colors.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 1-2","pages":"269 - 322"},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-024-00112-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Additive mappings on von Neumann algebras acting as Lie triple centralizer via local actions and related mappings 通过局部作用和相关映射充当列三中心子的冯-诺依曼布拉上的加法映射
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-03-21 DOI: 10.1007/s44146-024-00123-z
Behrooz Fadaee, Hoger Ghahramani
{"title":"Additive mappings on von Neumann algebras acting as Lie triple centralizer via local actions and related mappings","authors":"Behrooz Fadaee,&nbsp;Hoger Ghahramani","doi":"10.1007/s44146-024-00123-z","DOIUrl":"10.1007/s44146-024-00123-z","url":null,"abstract":"<div><p>Let <span>( {mathcal {M}} )</span> be an arbitrary von Neumann algebra, and <span>( phi : {mathcal {M}} rightarrow {mathcal {M}} )</span> be an additive map. We show that <span>(phi )</span> satisfies </p><div><div><span>$$begin{aligned} phi ([ [A, B], C ]) = [ [phi (A), B], C ] = [ [ A, phi (B) ], C ] end{aligned}$$</span></div></div><p>for all <span>(A,B, C in mathcal {M})</span> with <span>(AB=0)</span> if and only if <span>( phi (A) = W A + xi (A) )</span> for any <span>( A in {mathcal {M}} )</span>, where <span>( W in {textrm{Z}}( {mathcal {M}} ) )</span> and <span>( xi : {mathcal {M}} rightarrow {textrm{Z}}({mathcal {M}} ) )</span> is an additive mapping such that <span>(xi ([[A, B ], C] )=0)</span> for any <span>(A,B, C in mathcal {M})</span> with <span>(AB=0)</span>. Then we present various applications of this result to determine other types of additive mappings on von Neumann algebras such as Lie triple centralizers, Lie centralizers, generalized Lie triple derivations at zero products, generalized Lie derivations, Jordan centralizers and Jordan generalized derivations. Some of our results are generalizations of some previously known results.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"195 - 212"},"PeriodicalIF":0.5,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140222521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Semi-compactness of Null almost L-weakly and Null almost M-weakly compact operators 近乎 L 弱和近乎 M 弱空紧凑算子的半紧凑性
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-03-15 DOI: 10.1007/s44146-024-00107-z
Safae El filali, Khalid Bouras
{"title":"Semi-compactness of Null almost L-weakly and Null almost M-weakly compact operators","authors":"Safae El filali,&nbsp;Khalid Bouras","doi":"10.1007/s44146-024-00107-z","DOIUrl":"10.1007/s44146-024-00107-z","url":null,"abstract":"<div><p>In this paper, we investigate Banach lattices on which each positive semi-compact operator <span>(T: Erightarrow F)</span> is null almost L-weakly compact (rep. Null almost M-weakly compact). Additionally, we present certain sufficient and necessary conditions for a positive Null almost L-weakly compact operator to be semi-compact.\u0000</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 1-2","pages":"207 - 218"},"PeriodicalIF":0.5,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140239150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Norm inequalities for product of matrices 矩阵积的规范不等式
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-03-14 DOI: 10.1007/s44146-024-00121-1
Ahmad Al-Natoor
{"title":"Norm inequalities for product of matrices","authors":"Ahmad Al-Natoor","doi":"10.1007/s44146-024-00121-1","DOIUrl":"10.1007/s44146-024-00121-1","url":null,"abstract":"<div><p>In this paper, we prove some new norm inequalities for product of matrices. Among other results, we prove that if <i>A</i> and <i>B</i> are <i>n</i> <span>(times )</span> <i>n</i> complex matrices, then </p><div><div><span>$$begin{aligned} left| left| left| text { }left| AB^{*}right| ^{2}right| right| right| le min (left| left| left| B^{*}Bright| right| right| left| A^{*}Aright| ,left| left| left| A^{*}Aright| right| right| left| B^{*}Bright| ). end{aligned}$$</span></div></div><p>In particular, if <span>(left| left| left| cdot right| right| right| =left| cdot right| ,)</span> then </p><div><div><span>$$begin{aligned} left| AB^{*}right| ^{2}le left| A^{*}Aright| left| B^{*}Bright| , end{aligned}$$</span></div></div><p>which is known as the Cauchy–Schwarz inequality. Also, we prove that if <i>A</i> and <i>B</i> are <i>n</i> <span>(times )</span> <i>n</i> complex matrices,  then </p><div><div><span>$$begin{aligned} text { }left| AB^{*}right| ^{2}le wleft( A^{*}AB^{*}Bright) , end{aligned}$$</span></div></div><p>which is a refinement of the above Cauchy–Schwarz inequality. Here <span>( left| left| left| cdot right| right| right| ,)</span> <span>(left| cdot right| ,)</span> and <span>(w(cdot ))</span> denote any unitarily invariant norm, the spectral norm, and the numerical radius of matrices, respectively.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"153 - 160"},"PeriodicalIF":0.5,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140243630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to: Strongly convex matrix functions 修正：强凸矩阵函数
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-03-13 DOI: 10.1007/s44146-024-00122-0
Takashi Sano
{"title":"Correction to: Strongly convex matrix functions","authors":"Takashi Sano","doi":"10.1007/s44146-024-00122-0","DOIUrl":"10.1007/s44146-024-00122-0","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"691 - 692"},"PeriodicalIF":0.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Singular value inequalities with applications to norms and means of matrices 奇异值不等式在矩阵规范和均值中的应用
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-03-08 DOI: 10.1007/s44146-024-00113-1
Fuad Kittaneh, Hamid Reza Moradi, Mohammad Sababheh
{"title":"Singular value inequalities with applications to norms and means of matrices","authors":"Fuad Kittaneh,&nbsp;Hamid Reza Moradi,&nbsp;Mohammad Sababheh","doi":"10.1007/s44146-024-00113-1","DOIUrl":"10.1007/s44146-024-00113-1","url":null,"abstract":"<div><p>In this paper, we obtain some upper bounds for the singular values of sums of product of matrices. The obtained forms involve direct sums and mean-like matrix quantities. As applications, several bounds will be found in terms of the Aluthge transform, matrix means, matrix monotone functions and accretive-dissipative matrices. For example, we show that if <i>X</i> is an <span>(ntimes n)</span> accretive-dissipative matrix, then </p><div><div><span>$$begin{aligned} {{s}_{j}}left( X right) le left( 1+frac{sqrt{2}}{2} right) {{s}_{j}}left( Re Xoplus Im X right) , end{aligned}$$</span></div></div><p>for <span>(j=1,2,ldots n)</span>, where <span>(s_j(cdot ), Re (cdot ))</span> and <span>(Im (cdot ))</span> denote the <span>(j-)</span>th singular value, the real part and the imaginary part, respectively. We also show that if <span>(sigma _f,sigma _g)</span> are two matrix means corresponding to the operator monotone functions <i>f</i>, <i>g</i>, then </p><div><div><span>$$begin{aligned} {{s}_{j}}left( A{{sigma }_{f}}B-A{{sigma }_{g}}B right) le left| A right| {{s}_{j}}left( fleft( {{A}^{-frac{1}{2}}}B{{A}^{-frac{1}{2}}} right) oplus gleft( {{A}^{-frac{1}{2}}}B{{A}^{-frac{1}{2}}} right) right) , end{aligned}$$</span></div></div><p>for <span>(j =1,2, ldots , n)</span>, where <i>A</i>, <i>B</i> are two positive definite <span>(ntimes n)</span> matrices.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"419 - 439"},"PeriodicalIF":0.5,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140396789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Boundary values of pluriharmonic functions with Bott-Chern cohomology 具有 Bott-Chern 同调的多谐函数的边界值
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-02-28 DOI: 10.1007/s44146-024-00110-4
Sény Diatta, Souhaibou Sambou, Eramane Bodian, Salomon Sambou, Shaban Khidr
{"title":"Boundary values of pluriharmonic functions with Bott-Chern cohomology","authors":"Sény Diatta,&nbsp;Souhaibou Sambou,&nbsp;Eramane Bodian,&nbsp;Salomon Sambou,&nbsp;Shaban Khidr","doi":"10.1007/s44146-024-00110-4","DOIUrl":"10.1007/s44146-024-00110-4","url":null,"abstract":"<div><p>The main purpose of this paper is to investigate the relationship between continuation of pluriharmonic functions from the boundary of an unbounded domain and the vanishing of the Bott-Chern cohomology with supports in a paracompactifying family of closed subset of a complex manifold <i>X</i>. We moreover give a relation between distributional boundary values and extensible currents.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 1-2","pages":"231 - 239"},"PeriodicalIF":0.5,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140418786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterization of closed n-paranormal and (n^{*})-paranormal operators 封闭 n-paranormal 和 $$n^{*}$$ n ∗ -paranormal 算子的特征
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-02-26 DOI: 10.1007/s44146-024-00109-x
Salah Mecheri, Aissa Nasli Bakir
{"title":"Characterization of closed n-paranormal and (n^{*})-paranormal operators","authors":"Salah Mecheri,&nbsp;Aissa Nasli Bakir","doi":"10.1007/s44146-024-00109-x","DOIUrl":"10.1007/s44146-024-00109-x","url":null,"abstract":"<div><p>We give several basic and spectral properties of classes of closed <i>n</i>-paranormal and closed <span>(n^{*})</span>-paranormal operators on dense domains in complex separable Hilbert spaces. We prove that for both of these classes of operators, the null space of <span>((T-mu I))</span> and the range of <span>(R(E_{mu }))</span> are identical, where <span>(E_{mu })</span> is the Riesz projection with respect to an isolated point <span>(mu )</span> of the spectrum. We show that they satisfy Weyl’s theorem. Certain properties related to the reduced minimum modulus are also established.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 1-2","pages":"219 - 230"},"PeriodicalIF":0.5,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140431414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some results on unbounded absolute weak convergence 关于无约束绝对弱收敛的一些结果
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-02-25 DOI: 10.1007/s44146-024-00111-3
Houda Moktafi, Hassan Khabaoui, Kamal El Fahri
{"title":"Some results on unbounded absolute weak convergence","authors":"Houda Moktafi,&nbsp;Hassan Khabaoui,&nbsp;Kamal El Fahri","doi":"10.1007/s44146-024-00111-3","DOIUrl":"10.1007/s44146-024-00111-3","url":null,"abstract":"<div><p>In this paper, we establish the stability of uaw-convergence under passing from sublattices. The various implications of this fact are presented through the paper. In particular, we show that if <span>((x_{alpha }))</span> is an increasing net in a Banach lattice <i>E</i> and <span>(x_{alpha }overset{uaw}{longrightarrow }0)</span> in <i>E</i> then <span>(x_{alpha }overset{un}{longrightarrow }0)</span> in <span>(E^{''})</span>. Furthermore, we deduce some results concerning uaw-completeness. Additionally, we present a new characterizations of KB-spaces (resp. reflexive Banach lattices), using the concepts of uaw-convergence and un-convergence.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 1-2","pages":"241 - 250"},"PeriodicalIF":0.5,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140432404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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