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Maps preserving some spectral domains of Jordan product of operators 保留算子约当积谱域的映射
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-09-28 DOI: 10.1007/s44146-023-00096-5
Mhamed Elhodaibi, Somaya Saber
{"title":"Maps preserving some spectral domains of Jordan product of operators","authors":"Mhamed Elhodaibi,&nbsp;Somaya Saber","doi":"10.1007/s44146-023-00096-5","DOIUrl":"10.1007/s44146-023-00096-5","url":null,"abstract":"<div><p>Let <i>X</i> be an infinite-dimensional complex Banach space and let <span>(mathcal {B}(X))</span> denote the algebra of all bounded linear operators on <i>X</i>. For an operator <span>(T in mathcal {B}(X))</span> the sets <span>(sigma _{1}(T), sigma _{2}(T),)</span> and <span>(sigma _{3}(T))</span> are called, respectively, the semi-Fredholm domain, the Fredholm domain, and the Weyl domain, of <i>T</i> in the spectrum, <span>(sigma (T))</span>. Given <span>(i in {1,2,3})</span>, the goal of this article is to describe the general form of all surjective maps <span>(phi )</span> on <span>(mathcal {B}(X))</span> which satisfy </p><div><div><span>$$begin{aligned} sigma _{i}(phi (A)phi (T) +phi (T)phi (A)) = sigma _{i}(AT + TA) end{aligned}$$</span></div></div><p>for all <span>(A, T in mathcal {B}(X))</span>.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"621 - 634"},"PeriodicalIF":0.5,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135385593","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
Nonself (E_{f,g})-contractions on metrically convex metric spaces and their common fixed points 非自性$$E_{f,g}$$ -度量凸度量空间及其公共不动点上的收缩
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-09-21 DOI: 10.1007/s44146-023-00094-7
Hamid Shayanpour
{"title":"Nonself (E_{f,g})-contractions on metrically convex metric spaces and their common fixed points","authors":"Hamid Shayanpour","doi":"10.1007/s44146-023-00094-7","DOIUrl":"10.1007/s44146-023-00094-7","url":null,"abstract":"<div><p>In this paper, we define the new concept of <span>(E_{f,g})</span>-contraction mapping and check common fixed point theorems for such contractions in metrically convex metric spaces. We provide an example to support the presented results.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"611 - 619"},"PeriodicalIF":0.5,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136136240","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
Weakening of a local Bollobás type property and geometry of Banach spaces 局部波尔洛巴斯类型属性的弱化与巴拿赫空间的几何学
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-09-18 DOI: 10.1007/s44146-023-00095-6
Uday Shankar Chakraborty
{"title":"Weakening of a local Bollobás type property and geometry of Banach spaces","authors":"Uday Shankar Chakraborty","doi":"10.1007/s44146-023-00095-6","DOIUrl":"10.1007/s44146-023-00095-6","url":null,"abstract":"<div><p>This paper deals with a weaker form of the property so called <span>({textbf {L}}_{o,o})</span> for operators, which we call the property weak <span>({textbf {L}}_{o,o})</span> for operators. We characterize this property in terms of convergence of approximate norm attainment sets and prove that a pair of Banach spaces (<i>X</i>, <i>Y</i>) satisfies the property weak <span>({textbf {L}}_{o,o})</span> for compact operators if and only if <i>X</i> is reflexive. We further investigate the property weak <span>({textbf {L}}_{o,o})</span> for bilinear maps and obtain a connection of it with the property weak <span>({textbf {L}}_{o,o})</span> for operators. Importantly, we also characterize some geometric properties of Banach spaces with the help of convergence of approximate norm attainment sets.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 1-2","pages":"91 - 108"},"PeriodicalIF":0.5,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135153458","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
Maps on Grassmann spaces preserving the minimal principal angle 格拉斯曼空间上保留最小主角的映射
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-07-04 DOI: 10.1007/s44146-023-00093-8
Peter Šemrl
{"title":"Maps on Grassmann spaces preserving the minimal principal angle","authors":"Peter Šemrl","doi":"10.1007/s44146-023-00093-8","DOIUrl":"10.1007/s44146-023-00093-8","url":null,"abstract":"<div><p>Let <i>n</i> be a positive integer and <i>H</i> a Hilbert space. The description of the general form of bijective maps on the set of <i>n</i>-dimensional subspaces of <i>H</i> preserving the maximal principal angle has been obtained recently. This is a generalization of Wigner’s unitary-antiunitary theorem. In this paper we will obtain another extension of Wigner’s theorem in which the maximal principal angle is replaced by the minimal one. Moreover, in this case we do not need the bijectivity assumption.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 1-2","pages":"109 - 122"},"PeriodicalIF":0.5,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-023-00093-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86676193","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 the monogenity of pure quartic relative extensions of ({{mathbb {Q}}}(i)) 的纯四次相对扩展的单一性 $${{mathbb {Q}}}(i)$$
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-06-14 DOI: 10.1007/s44146-023-00092-9
István Gaál, László Remete
{"title":"On the monogenity of pure quartic relative extensions of ({{mathbb {Q}}}(i))","authors":"István Gaál,&nbsp;László Remete","doi":"10.1007/s44146-023-00092-9","DOIUrl":"10.1007/s44146-023-00092-9","url":null,"abstract":"<div><p>We consider pure quartic relative extensions of the number field <span>({{mathbb {Q}}}(i))</span> of type <span>(K={{mathbb {Q}}}(root 4 of {a+bi}))</span>, where <span>(a,bin {{mathbb {Z}}})</span> and <span>(bne 0)</span>, such that <span>(a+biin {{mathbb {Z}}}[i])</span> is square-free. We describe integral bases of these fields. The index form equation is reduced to a relative cubic Thue equation over <span>({{mathbb {Q}}}(i))</span> and some corresponding quadratic form equations. We consider monogenity of <i>K</i> and relative monogenity of <i>K</i> over <span>({{mathbb {Q}}}(i))</span>. We shall show how our former method based on the factors of the index form can be used in the relative case to exclude relative monogenity in some cases.\u0000</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"357 - 371"},"PeriodicalIF":0.5,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-023-00092-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87086836","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 integral extensions of Banach algebras 关于Banach代数的积分扩展
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-06-08 DOI: 10.1007/s44146-023-00091-w
Sara El Kinani, Rachid Choukri
{"title":"On integral extensions of Banach algebras","authors":"Sara El Kinani,&nbsp;Rachid Choukri","doi":"10.1007/s44146-023-00091-w","DOIUrl":"10.1007/s44146-023-00091-w","url":null,"abstract":"<div><p>We consider countable extensions of commutative and unital Banach algebras. We study these Banach algebra structures with or without assuming the continuity of the canonical injection. We also prove that a countable extension endowed with a Banach algebra norm with continuous injection is actually a finite extension.\u0000</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"501 - 508"},"PeriodicalIF":0.5,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74300906","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
Béla Szőkefalvi-Nagy Medal 2022 2022年Béla Szõkefalvi Nagy奖章
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-05-27 DOI: 10.1007/s44146-023-00088-5
{"title":"Béla Szőkefalvi-Nagy Medal 2022","authors":"","doi":"10.1007/s44146-023-00088-5","DOIUrl":"10.1007/s44146-023-00088-5","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 1-2","pages":"1 - 2"},"PeriodicalIF":0.5,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50518378","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: Semigroups of composition operators on Hardy spaces of the half-plane 修正:半平面Hardy空间上复合算子的半群
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-05-26 DOI: 10.1007/s44146-023-00090-x
Athanasios G. Arvanitidis
{"title":"Correction to: Semigroups of composition operators on Hardy spaces of the half-plane","authors":"Athanasios G. Arvanitidis","doi":"10.1007/s44146-023-00090-x","DOIUrl":"10.1007/s44146-023-00090-x","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"635 - 635"},"PeriodicalIF":0.5,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136040157","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
The norming sets of ({{mathcal {L}}}(^2 {mathbb {R}}^2_{h(w)})) （｛mathcal｛L｝｝）｝（^2｛math bb｛R｝｝^2_｛h（w）｝）的规范集
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-05-09 DOI: 10.1007/s44146-023-00078-7
Sung Guen Kim
{"title":"The norming sets of ({{mathcal {L}}}(^2 {mathbb {R}}^2_{h(w)}))","authors":"Sung Guen Kim","doi":"10.1007/s44146-023-00078-7","DOIUrl":"10.1007/s44146-023-00078-7","url":null,"abstract":"<div><p>An element <span>((x_1, ldots , x_n)in E^n)</span> is called a <i>norming point</i> of <span>(Tin {{mathcal {L}}}(^n E))</span> if <span>(Vert x_1Vert =cdots =Vert x_nVert =1)</span> and <span>(|T(x_1, ldots , x_n)|=Vert TVert ,)</span> where <span>({{mathcal {L}}}(^n E))</span> denotes the space of all continuous <i>n</i>-linear forms on <i>E</i>. For <span>(Tin {{mathcal {L}}}(^n E),)</span> we define </p><div><div><span>$$begin{aligned} text {Norm}(T)={(x_1, ldots , x_n)in E^n: (x_1, ldots , x_n)~text{ is } text{ a } text{ norming } text{ point } text{ of }~T}. end{aligned}$$</span></div></div><p>Let <span>({mathbb {R}}^2_{h(w)})</span> denote the plane with the hexagonal norm with weight <span>(0&lt;w&lt;1)</span></p><div><div><span>$$begin{aligned} Vert (x, y)Vert _{h(w)}=max Big {|y|, |x|+(1-w)|y|Big }. end{aligned}$$</span></div></div><p>We classify <span>(text {Norm}(T))</span> for every <span>(Tin {{mathcal {L}}}(^2 {mathbb {R}}_{h(w)}^2))</span>.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 1-2","pages":"61 - 79"},"PeriodicalIF":0.5,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-023-00078-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50466860","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
Spectra of some weighted composition operators on the ball 球上一些加权组合算子的谱
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2023-05-04 DOI: 10.1007/s44146-023-00089-4
Scott Kaschner, Trieu Le, Chloe Makdad, Benjamin Rempfer, Derek Thompson, DeJuan Winters
{"title":"Spectra of some weighted composition operators on the ball","authors":"Scott Kaschner,&nbsp;Trieu Le,&nbsp;Chloe Makdad,&nbsp;Benjamin Rempfer,&nbsp;Derek Thompson,&nbsp;DeJuan Winters","doi":"10.1007/s44146-023-00089-4","DOIUrl":"10.1007/s44146-023-00089-4","url":null,"abstract":"<div><p>We find sufficient conditions for a self-map of the unit ball to converge uniformly under iteration to a fixed point or idempotent on the entire ball. Using these tools, we establish spectral containments for weighted composition operators on Hardy and Bergman spaces of the ball. When the compositional symbol is in the Schur–Agler class, we establish the spectral radii of these weighted composition operators.\u0000</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"89 3-4","pages":"373 - 387"},"PeriodicalIF":0.5,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87439967","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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