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Advances in Operator Theory最新文献

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Boundedness of operators generated by fractional heat semigroups related to Schrödinger operators on stratified Lie groups via T1 theorem 与Schrödinger算子相关的分数热半群在分层李群上的有界性
IF 0.7
Advances in Operator Theory Pub Date : 2025-11-04 DOI: 10.1007/s43036-025-00484-4
Chuanhong Sun, Pengtao Li, Zengjian Lou
{"title":"Boundedness of operators generated by fractional heat semigroups related to Schrödinger operators on stratified Lie groups via T1 theorem","authors":"Chuanhong Sun,&nbsp;Pengtao Li,&nbsp;Zengjian Lou","doi":"10.1007/s43036-025-00484-4","DOIUrl":"10.1007/s43036-025-00484-4","url":null,"abstract":"<div><p>Let <span>(L=-{Delta }_{{mathbb {G}} }+V)</span> be a Schrödinger operator on the stratified Lie group <span>({mathbb {G}},)</span> where <span>({Delta }_{{mathbb {G}} })</span> is the sub-Laplacian and the nonnegative potential <i>V</i> belongs to the reverse Hölder class <span>(B_{q}, qge {mathcal {Q}}/2,)</span> in which <span>({mathcal {Q}})</span> is the homogeneous dimension of <span>({mathbb {G}}.)</span> In this article, we firstly study the fractional heat semigroups <span>({e^{-tL^{alpha }}}_{t&gt;0})</span> with <span>(alpha &gt;0)</span> associated with <i>L</i>. Subsequently, the regularities of the fractional heat semigroup is estimated with the use of the subordinative formula. Furthermore, in terms of application, we establish the <span>(BMO_{L}^{gamma }({mathbb {G}}))</span>-boundedness of the maximal function and the Littlewood–Paley <span>({mathfrak {g}})</span>-functions related with the Schrödinger operator <i>L</i> by <i>T</i>1 theorem, respectively.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456484","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
On C-quasinormal operators 关于c -拟正规算子
IF 0.7
Advances in Operator Theory Pub Date : 2025-11-03 DOI: 10.1007/s43036-025-00482-6
Eungil Ko, Ji Eun Lee, Mee-Jung Lee
{"title":"On C-quasinormal operators","authors":"Eungil Ko,&nbsp;Ji Eun Lee,&nbsp;Mee-Jung Lee","doi":"10.1007/s43036-025-00482-6","DOIUrl":"10.1007/s43036-025-00482-6","url":null,"abstract":"<div><p>An operator <span>(Tin {{mathcal {L}}}({{mathcal {H}}}))</span> is called <i>conjugation-quasinormal</i> if there is a conjugation <i>C</i> on an infinite-dimensional complex Hilbert space <span>({{mathcal {H}}})</span> such that <span>([CT,T^{*}T]=0)</span> where <span>([R,S]:=RS-SR)</span>. In particular, if such a conjugation <i>C</i> is specified, an operator <i>T</i> is said to be <i>C</i>-quasinormal. In this paper, we study various properties of conjugation-quasinormal operators. Especially, we provide several characterizations of conjugation-quasinormal operators. Moreover, if <i>T</i> is a partial isometry, we show that <i>T</i> is <i>C</i>-hyponormal if and only if <i>T</i> is <i>C</i>-quasinormal. Finally, we consider conjugation-operator transforms.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456155","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 Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces 均匀光滑Banach空间上随机半群的强大数律
IF 0.7
Advances in Operator Theory Pub Date : 2025-11-03 DOI: 10.1007/s43036-025-00481-7
Sviatoslav V. Dzhenzher, Vsevolod Zh. Sakbaev
{"title":"The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces","authors":"Sviatoslav V. Dzhenzher,&nbsp;Vsevolod Zh. Sakbaev","doi":"10.1007/s43036-025-00481-7","DOIUrl":"10.1007/s43036-025-00481-7","url":null,"abstract":"<div><p>We consider random linear continuous operators <span>(Omega rightarrow {mathcal {L}}({mathcal {X}}, {mathcal {X}}))</span> on a Banach space <span>({mathcal {X}}.)</span> For example, such random operators may be random quantum channels. The Law of Large Numbers is known when <span>({mathcal {X}})</span> is a Hilbert space, in the form of the usual Law of Large Numbers for random operators, and in some other particular cases. Instead of the sum of i.i.d. variables, there may be considered the composition of random semigroups <span>(e^{A_i t/n}.)</span> We obtain the Strong Law of Large Numbers in Strong Operator Topology for random semigroups of bounded linear operators on a uniformly smooth Banach space. We also develop another approach giving the SLLN in Weak Operator Topology for all Banach spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456156","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 operator (C_{phi }^*C_{psi }) when (phi ) is a Blaschke product 当(phi )为Blaschke产品时，操作符为(C_{phi }^*C_{psi })
IF 0.7
Advances in Operator Theory Pub Date : 2025-10-24 DOI: 10.1007/s43036-025-00476-4
John H. Clifford, Michael Dabkowski, Alan Wiggins, Yunus Zeytuncu
{"title":"The operator (C_{phi }^*C_{psi }) when (phi ) is a Blaschke product","authors":"John H. Clifford,&nbsp;Michael Dabkowski,&nbsp;Alan Wiggins,&nbsp;Yunus Zeytuncu","doi":"10.1007/s43036-025-00476-4","DOIUrl":"10.1007/s43036-025-00476-4","url":null,"abstract":"<div><p>For <span>(phi )</span> and <span>(psi )</span> inner functions that fix the origin on the open unit disk <span>(mathbb {D})</span> in the complex plane, we consider the question of whether the associated linear operator <span>(C_{phi }^*C_{psi })</span> can be compact or finite-rank on <span>(H^2(mathbb {D}))</span>. We show that <span>(C_{phi }^*C_{psi })</span> cannot be rank-one when <span>(phi )</span> has purely atomic Aleksandrov–Clark measure and <span>(psi )</span> extends continuously to the boundary of <span>(mathbb {D})</span>. When <span>(phi )</span> and <span>(psi )</span> are finite Blaschke products each with two distinct factors, we show <span>(C_{phi }^*C_{psi })</span> cannot be compact. Finally, following work of Cowen and MacCluer, we characterize the range of <span>(C_{phi }^*)</span> when <span>(phi )</span> is a Blaschke product.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352298","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
A Lie–Trotter type formula for q-exponential operators q-指数算子的Lie-Trotter型公式
IF 0.7
Advances in Operator Theory Pub Date : 2025-10-21 DOI: 10.1007/s43036-025-00477-3
Dumitru Popa
{"title":"A Lie–Trotter type formula for q-exponential operators","authors":"Dumitru Popa","doi":"10.1007/s43036-025-00477-3","DOIUrl":"10.1007/s43036-025-00477-3","url":null,"abstract":"<div><p>We prove a Lie–Trotter type formula for <i>q</i>-exponential operators: </p><div><div><span>$$begin{aligned} lim limits _{nrightarrow infty }left[ left( I+left( 1-qright) frac{U}{ n}right) ^{frac{1}{1-q}}left( I+left( 1-qright) frac{V}{n}right) ^{ frac{1}{1-q}}right] ^{n}=e^{U+V} end{aligned}$$</span></div></div><p>where <i>E</i> is a Banach space, <i>U</i>, <i>V</i> bounded linear operators on <i>E</i> and <span>(qin mathbb {R})</span>, <span>(qne 1)</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145327526","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
Properties of one-sided generalized Drazin inverses in Banach algebras Banach代数中单侧广义Drazin逆的性质
IF 0.7
Advances in Operator Theory Pub Date : 2025-10-21 DOI: 10.1007/s43036-025-00479-1
Milica Z. Kolundžija, Dijana Mosić
{"title":"Properties of one-sided generalized Drazin inverses in Banach algebras","authors":"Milica Z. Kolundžija,&nbsp;Dijana Mosić","doi":"10.1007/s43036-025-00479-1","DOIUrl":"10.1007/s43036-025-00479-1","url":null,"abstract":"<div><p>New characterizations of left and right generalized Drazin inverses are presented in Banach algebra using tripotents. We explore Cline’s formula for those inverses. Also, we find the conditions under which the product of two left (or right) generalized Drazin invertible elements has the appropriate one-sided generalized Drazin inverse. Consequently, we study when the sum of two zero product elements has a one-sided generalized Drazin inverse. Perturbation results for the left (or right) generalized Drazin inverse are also investigated. Applying our results, we obtain new properties of the left (or right) Drazin inverse and recover known results about the generalized Drazin inverse.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145352706","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
Generalized entropy numbers of sets and operators 集合和算子的广义熵数
IF 0.7
Advances in Operator Theory Pub Date : 2025-09-24 DOI: 10.1007/s43036-025-00474-6
Eduardo Brandani da Silva, Luan Carlos Della Pasqua
{"title":"Generalized entropy numbers of sets and operators","authors":"Eduardo Brandani da Silva,&nbsp;Luan Carlos Della Pasqua","doi":"10.1007/s43036-025-00474-6","DOIUrl":"10.1007/s43036-025-00474-6","url":null,"abstract":"<div><p>In this work, we introduce and study generalized entropy numbers for sets and operators acting on Banach spaces. The classical notion of Hausdorff entropy numbers becomes a particular case of the given definition. We also provide several other examples of generalized entropy numbers for sets and operators. We prove several properties for the general case.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168633","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
Notes on non-compact maps and the importance of Bernstein numbers 关于非紧图的注释和伯恩斯坦数的重要性
IF 0.7
Advances in Operator Theory Pub Date : 2025-09-18 DOI: 10.1007/s43036-025-00456-8
David E. Edmunds, Jan Lang
{"title":"Notes on non-compact maps and the importance of Bernstein numbers","authors":"David E. Edmunds,&nbsp;Jan Lang","doi":"10.1007/s43036-025-00456-8","DOIUrl":"10.1007/s43036-025-00456-8","url":null,"abstract":"<div><p>In this review paper we study non-compact operators and embeddings between function spaces, highlighting interesting phenomena and the significance of Bernstein numbers. In particular, we demonstrate that for non-compact maps the usual <i>s</i>-numbers (e.g., approximation, Kolmogorov, and entropy numbers) fail to reveal finer structural properties, and one must instead consider concepts such as strict singularity and Bernstein numbers.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145073980","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
Linearization and Lemma of Newton for operator functions 算子函数的线性化和牛顿引理
IF 0.7
Advances in Operator Theory Pub Date : 2025-09-03 DOI: 10.1007/s43036-025-00472-8
Matthias Stiefenhofer
{"title":"Linearization and Lemma of Newton for operator functions","authors":"Matthias Stiefenhofer","doi":"10.1007/s43036-025-00472-8","DOIUrl":"10.1007/s43036-025-00472-8","url":null,"abstract":"<div><p>We study the action of the nonlinear mapping <i>G</i>[<i>z</i>] between real or complex Banach spaces in the vicinity of a given curve with respect to possible linearization, emerging patterns of level sets, as well as existing solutions of <span>(G[z]=0)</span>. The results represent local generalizations of the standard implicit or inverse function theorem and of Newton’s Lemma, considering the order of approximation needed to obtain solutions of <span>(G[z]=0)</span>. The main technical tool is given by Jordan chains with increasing rank, used to obtain an Ansatz, appropriate for transformation of the nonlinear system to its linear part. The family of linear mappings is restricted to the case of an isolated singularity. Geometrically, the Jordan chains define a generalized cone around the given curve, composed of approximate solutions of order 2<i>k</i> with <i>k</i> denoting the maximal rank of Jordan chains needed to ensure <i>k</i>-surjectivity of the linear family. Along these lines, the zero set of <i>G</i>[<i>z</i>] in the cone is calculated immediately, agreeing up to the order of <span>(k-1)</span> with the given approximation. Hence, the results may also be interpreted as a version of Tougeron’s implicit function theorem in Banach spaces, essentially restricted to the arc case of a single variable. Finally, by considering a left shift of the Jordan chains, the Ansatz can be modified in a systematic way to obtain a sequence of refined versions of linearization theorems and Newton Lemmas in Banach spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00472-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934611","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
Maps preserving the dimension of fixed points of Jordan triple product of operators 保持算子的约旦三重积不动点维数的映射
IF 0.7
Advances in Operator Theory Pub Date : 2025-08-27 DOI: 10.1007/s43036-025-00473-7
Rixia Song, Weijuan Shi
{"title":"Maps preserving the dimension of fixed points of Jordan triple product of operators","authors":"Rixia Song,&nbsp;Weijuan Shi","doi":"10.1007/s43036-025-00473-7","DOIUrl":"10.1007/s43036-025-00473-7","url":null,"abstract":"<div><p>Let <span>({mathcal {X}})</span> be a complex Banach space, and let <span>({mathcal {B}}({mathcal {X}}))</span> be the algebra of all bounded linear operators on <span>({mathcal {X}}.)</span> In this paper, we characterize the general forms of surjective maps on <span>({mathcal {B}}({mathcal {X}}))</span> that preserve the dimension of fixed points of Jordan triple product of operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144909834","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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