ACTA SCIENTIARUM MATHEMATICARUM最新文献_第8页

Inequalities for functions of (2times 2) block matrices 块矩阵函数的不等式

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-04-13 DOI: 10.1007/s44146-023-00082-x

Fadi Alrimawi

{"title":"Inequalities for functions of (2times 2) block matrices","authors":"Fadi Alrimawi","doi":"10.1007/s44146-023-00082-x","DOIUrl":"10.1007/s44146-023-00082-x","url":null,"abstract":"<div>Let (T=left[ begin{array}{cc} T_{11} &{} T_{12} T_{21} &{} T_{22} end{array} right] ) be accretive-dissipative, where (T_{11},T_{12},T_{21},) and (T_{22} ) are (ntimes n) complex matrices. Let f be a non-negative function on ( [0,infty )) such that (f(0)=0), and let (alpha ,beta in (0,1)) such that (alpha +beta =1). For every unitarily invariant norm (left| left| left| cdot right| right| right| ), it is shown that <div><div>$$begin{aligned} sum _{j=1}^{2}left| left| left| fleft( frac{left| T_{jj}+(2alpha -1)T_{jj}^{*}right| }{2sqrt{2}}right) +fleft( sqrt{frac{alpha beta }{2}}left| T_{jj}^{*}right| right) right| right| right| le 2max (alpha ,beta )left| left| left| f(left| Tright| )right| right| right| end{aligned}$$</div></div>whenever (trightarrow fleft( sqrt{t}right) ) is convex and <div><div>$$begin{aligned} sum _{j=1}^{2}left| left| left| alpha fleft( frac{ left| T_{jj}+(2alpha -1)T_{jj}^{*}right| }{sqrt{2alpha }} right) +beta fleft( sqrt{2alpha }left| T_{jj}^{*}right| right) right| right| right| le 4left| left| left| fleft( sqrt{ max (alpha ,beta )}left| Tright| right) right| right| right| end{aligned}$$</div></div>whenever f is concave.</div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 1-2","pages":"23 - 33"},"PeriodicalIF":0.5,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50476955","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

Certain Bernstein-type (L_p) inequalities for polynomials 多项式的某些bernstein型$$L_p$$ L p不等式

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-04-12 DOI: 10.1007/s44146-023-00074-x

N. A. Rather, Aijaz Bhat, Suhail Gulzar

引用次数: 0

Unitarily invariant norms on finite von Neumann algebras 有限von Neumann代数上的酉不变范数

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-04-03 DOI: 10.1007/s44146-023-00075-w

Haihui Fan, Don Hadwin

引用次数: 0

Analyticity, rank one perturbations and the invariance of the left spectrum 分析性，一级扰动和左谱的不变性

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-04-01 DOI: 10.1007/s44146-023-00076-9

Sameer Chavan, Soumitra Ghara, Paramita Pramanick

{"title":"Analyticity, rank one perturbations and the invariance of the left spectrum","authors":"Sameer Chavan, Soumitra Ghara, Paramita Pramanick","doi":"10.1007/s44146-023-00076-9","DOIUrl":"10.1007/s44146-023-00076-9","url":null,"abstract":"<div>We discuss the question of the analyticity of a rank one perturbation of an analytic operator. If ({mathscr {M}}_z) is the bounded operator of multiplication by z on a functional Hilbert space ({mathscr {H}}_kappa ) and (f in {mathscr {H}}) with (f(0)=0,) then ({mathscr {M}}_z + f otimes 1) is always analytic. If (f(0) ne 0,) then the analyticity of ({mathscr {M}}_z + f otimes 1) is characterized in terms of the membership to ({mathscr {H}}_kappa ) of the formal power series obtained by multiplying f(z) by (frac{1}{f(0)-z}.) As an application, we discuss the problem of the invariance of the left spectrum under rank one perturbation. In particular, we show that the left spectrum (sigma _l(T + f otimes g)) of the rank one perturbation (T + f otimes g,) (,g in ker (T^*),) of a cyclic analytic left invertible bounded linear operator T coincides with the left spectrum of T except the point (langle {f},,{g} rangle .) In general, the point (langle {f},,{g} rangle ) may or may not belong to (sigma _l(T + f otimes g).) However, if it belongs to (sigma _l(T + f otimes g) backslash {0},) then it is a simple eigenvalue of (T + f otimes g).</div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"559 - 571"},"PeriodicalIF":0.5,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89278620","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

Beurling’s theorem for the Hardy operator on (L^2[0,1]) $$L^2[0,1]$$ l2上Hardy算子的Beurling定理[0]

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-03-18 DOI: 10.1007/s44146-023-00073-y

Jim Agler, John E. McCarthy

引用次数: 2

Representations of generalized Hardy functions in Beurling’s tempered distributions 广义Hardy函数在beurling缓律分布中的表示

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-03-16 DOI: 10.1007/s44146-023-00061-2

Byung Keun Sohn

引用次数: 0

On the perturbation of pseudo-generalized invertible operators 伪广义可逆算子的摄动

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-03-06 DOI: 10.1007/s44146-023-00068-9

Asma Lahmar, Haïkel Skhiri

引用次数: 0

Partial isometries and generalized inverses of linear relations 线性关系的偏等距与广义逆

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-03-05 DOI: 10.1007/s44146-023-00067-w

Zied Garbouj

引用次数: 0

Some best approximation theorems and best proximity point theorems 一些最佳逼近定理和最佳邻近点定理

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-03-05 DOI: 10.1007/s44146-023-00065-y

S. Sadiq Basha

{"title":"Some best approximation theorems and best proximity point theorems","authors":"S. Sadiq Basha","doi":"10.1007/s44146-023-00065-y","DOIUrl":"10.1007/s44146-023-00065-y","url":null,"abstract":"<div>A best approximation theorem for almost cyclic contractions has been proved in the recent article (Sadiq Basha in J. Fixed Point Theory Appl 23:32, 2021). The purpose of this note is to show that, with the same hypotheses as in the preceding best approximation theorem, the conclusion of the theorem can be strengthened to produce a best proximity point rather than a best approximation and hence a best proximity point theorem for almost cyclic contractions in the framework of a uniformly convex Banach space. Further, it is interesting to observe that such a best proximity point theorem for almost cyclic contractions generalizes/subsumes the well known best proximity point theorem, due to Eldred and Veeramani (J Math Anal Appl 323:1001–1006, 2006), for cyclic contractions in the framework of a uniformly convex Banach space. On the other hand, these best approximation theorems and best proximity point theorems for some types of contractions do not generalize the most elegant Banach’s contraction principle because of the underlying richer framework of a uniformly convex Banach space rather than a simpler framework like a complete metric space. Therefore, the purpose of this note is to bring forth the framework of utmost complete space and establish a best proximity point theorem for almost cyclic contractions in such a simpler framework, thereby generalizing the contraction principle.\u0000</div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 1-2","pages":"215 - 226"},"PeriodicalIF":0.5,"publicationDate":"2023-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-023-00065-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50452956","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

On some questions for the q-integration operator 关于q-积分算子的几个问题

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ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-03-04 DOI: 10.1007/s44146-023-00064-z

Mubariz T. Garayev

引用次数: 0