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Advances in Operator Theory最新文献

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Spectral reconstruction of operator tuples 算子元组的频谱重构
IF 0.8
Advances in Operator Theory Pub Date : 2024-09-10 DOI: 10.1007/s43036-024-00380-3
Michael I. Stessin
{"title":"Spectral reconstruction of operator tuples","authors":"Michael I. Stessin","doi":"10.1007/s43036-024-00380-3","DOIUrl":"10.1007/s43036-024-00380-3","url":null,"abstract":"<div><p>The spectral theorem implies that the spectrum of a bounded normal operator acting on a Hilbert space provides a substantial information about the operator. For example, the set of eigenvalues of a normal matrix and their respective multiplicities determine the matrix up to a unitary equivalence, while the spectral measure, <span>(E_B(lambda ))</span> of a normal operator <i>B</i> acting on a Hilbert space determines <i>B</i> via the integral spectral resolution, </p><div><div><span>$$begin{aligned} B=int _{sigma (B)} lambda dE_B(lambda ). end{aligned}$$</span></div></div><p>In general, for a non-normal operator the spectrum provides a rather limited information about the operator. In this paper we show that, if we include an arbitrary bounded operator <i>B</i> acting on a separable Hilbert space into a quadruple which contains 3 specific operators along with <i>B</i>, it is possible to reconstruct <i>B</i> from the proper projective joint spectrum of the quadruple (and here we mean reconstruct precisely, not up to an equivalence). We call this process <b>spectral reconstruction</b>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411243","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
Asymptotics of the eigenvalues of seven-diagonal Toeplitz matrices of a special form 特殊形式的七对角托普利兹矩阵特征值的渐近性
IF 0.8
Advances in Operator Theory Pub Date : 2024-09-04 DOI: 10.1007/s43036-024-00374-1
M. Barrera, S. Grudsky, V. Stukopin, I. Voronin
{"title":"Asymptotics of the eigenvalues of seven-diagonal Toeplitz matrices of a special form","authors":"M. Barrera,&nbsp;S. Grudsky,&nbsp;V. Stukopin,&nbsp;I. Voronin","doi":"10.1007/s43036-024-00374-1","DOIUrl":"10.1007/s43036-024-00374-1","url":null,"abstract":"<div><p>This work is devoted to the construction of a uniform asymptotics in the dimension of the matrix n tending to infinity of all eigenvalues in the case of a seven-diagonal Toeplitz matrix with a symbol having a zero of the sixth order, while the cases of symbols with zeros of the second and fourth orders were considered earlier. On the other hand, the results obtained refine the results of the classical work of Parter and Widom on the asymptotics of the extreme eigenvalues. We also note that the obtained formulas showed high computational efficiency both in sense of accuracy (already for relatively small values of n) and in sense of speed.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409895","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
Embedding theorems for Besov–Morrey spaces 贝索夫-莫雷空间的嵌入定理
IF 0.8
Advances in Operator Theory Pub Date : 2024-08-22 DOI: 10.1007/s43036-024-00377-y
Arash Ghorbanalizadeh, Tahereh Khazaee
{"title":"Embedding theorems for Besov–Morrey spaces","authors":"Arash Ghorbanalizadeh,&nbsp;Tahereh Khazaee","doi":"10.1007/s43036-024-00377-y","DOIUrl":"10.1007/s43036-024-00377-y","url":null,"abstract":"<div><p>The purpose of this paper is to investigate the embedding theorems for Besov–Morrey spaces using the equivalence theorem for the <i>K</i>-functional and the modulus of continuity on Morrey spaces. First, we obtain some theorems in ball Banach function space and then focus on Morrey spaces. The Marchaud’s inequality on Morrey spaces and a specific case of embedding theorems for Sobolev–Morrey spaces are crucial tools. We show that the Besov–Morrey space <span>(B_{alpha , a}^{p,lambda }(mathbb {R}^{n}))</span> is continuously embedded in the Morrey-Lorentz space <span>(mathcal {M}_{q,p}^{lambda }(mathbb {R}^{n}))</span>, and also, for any <span>(alpha , beta &gt; 0)</span> and <span>(1&lt; ale p &lt; q le infty )</span>, the Besov–Morrey space <span>(B_{alpha + beta , a}^{p,lambda }(mathbb {R}^{n}))</span> is continuously embedded in the Besov–Morrey space <span>(B_{beta , a}^{q,lambda }(mathbb {R}^{n}))</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413066","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
Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure 希尔伯特空间估值高斯过程及其核、因式分解和协方差结构
IF 0.8
Advances in Operator Theory Pub Date : 2024-08-19 DOI: 10.1007/s43036-024-00375-0
Palle E. T. Jorgensen, James Tian
{"title":"Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure","authors":"Palle E. T. Jorgensen,&nbsp;James Tian","doi":"10.1007/s43036-024-00375-0","DOIUrl":"10.1007/s43036-024-00375-0","url":null,"abstract":"<div><p>Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation constructions in operator theory, and the second to general classes of stochastic processes. For the latter, we apply our operator valued kernel-results in order to build new Hilbert space-valued Gaussian processes, and to analyze their structures of covariance configurations.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412366","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 (p, r, s)-summing Bloch maps and Lapresté norms 关于（p，r，s）求和布洛赫映射和拉普斯特规范
IF 0.8
Advances in Operator Theory Pub Date : 2024-08-16 DOI: 10.1007/s43036-024-00376-z
A. Belacel, A. Bougoutaia, A. Jiménez-Vargas
{"title":"On (p, r, s)-summing Bloch maps and Lapresté norms","authors":"A. Belacel,&nbsp;A. Bougoutaia,&nbsp;A. Jiménez-Vargas","doi":"10.1007/s43036-024-00376-z","DOIUrl":"10.1007/s43036-024-00376-z","url":null,"abstract":"<div><p>The theory of (<i>p</i>, <i>r</i>, <i>s</i>)-summing and (<i>p</i>, <i>r</i>, <i>s</i>)-nuclear linear operators on Banach spaces was developed by Pietsch in his book on operator ideals (Pietsch in Operator ideals, North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, 1980, Chapters 17 and 18) Due to recent advances in the theory of ideals of Bloch maps, we extend these concepts to Bloch maps from the complex open unit disc <span>(mathbb {D})</span> into a complex Banach space <i>X</i>. Variants for (<i>r</i>, <i>s</i>)-dominated Bloch maps of classical Pietsch’s domination and Kwapień’s factorization theorems of (<i>r</i>, <i>s</i>)-dominated linear operators are presented. We define analogues of Lapresté’s tensor norms on the space of <i>X</i>-valued Bloch molecules on <span>(mathbb {D})</span> to address the duality of the spaces of <span>((p^*,r,s))</span>-summing Bloch maps from <span>(mathbb {D})</span> into <span>(X^*)</span>. The class of (<i>p</i>, <i>r</i>, <i>s</i>)-nuclear Bloch maps is introduced and analysed to give examples of (<i>p</i>, <i>r</i>, <i>s</i>)-summing Bloch maps.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411999","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
Inverses of Toeplitz plus Hankel operators with generating matrix functions 具有生成矩阵函数的托普利兹加汉克尔算子的逆运算
IF 0.8
Advances in Operator Theory Pub Date : 2024-08-03 DOI: 10.1007/s43036-024-00373-2
Victor D. Didenko, Bernd Silbermann
{"title":"Inverses of Toeplitz plus Hankel operators with generating matrix functions","authors":"Victor D. Didenko,&nbsp;Bernd Silbermann","doi":"10.1007/s43036-024-00373-2","DOIUrl":"10.1007/s43036-024-00373-2","url":null,"abstract":"<div><p>The invertibility of Toeplitz plus Hankel operators <span>(T(mathcal {A})+H(mathcal {B}))</span>, <span>(mathcal {A},mathcal {B}in L^infty _{dtimes d}(mathbb {T}))</span> acting on vector Hardy spaces <span>(H^p_d(mathbb {T}))</span>, <span>(1&lt;p&lt;infty )</span>, is studied. Assuming that the generating matrix functions <span>(mathcal {A})</span> and <span>(mathcal {B})</span> satisfy the equation </p><div><div><span>$$begin{aligned} mathcal {B}^{-1} mathcal {A}= widetilde{mathcal {A}}^{-1}widetilde{mathcal {B}}, end{aligned}$$</span></div></div><p>where <span>(widetilde{mathcal {A}}(t):=mathcal {A}(1/t))</span>, <span>(widetilde{mathcal {B}}(t):=mathcal {B}(1/t))</span>, <span>(tin mathbb {T})</span>, we establish sufficient conditions for the one-sided invertibility and invertibility of the operators mentioned and construct the corresponding inverses. If <span>(d=1)</span>, the above equation reduces to the known matching condition, widely used in the study of Toeplitz plus Hankel operators with scalar generating functions.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409558","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
Pietsch type composition results for bilinear summing operators 双线性求和算子的 Pietsch 型组合结果
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-29 DOI: 10.1007/s43036-024-00372-3
Dumitru Popa
{"title":"Pietsch type composition results for bilinear summing operators","authors":"Dumitru Popa","doi":"10.1007/s43036-024-00372-3","DOIUrl":"10.1007/s43036-024-00372-3","url":null,"abstract":"<div><p>We prove some splitting results for bilinear summing operators and as a consequence Pietsch type composition results. Some examples are given.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00372-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414960","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
Interpolating inequalities for unitarily invariant norms of matrices 矩阵单位不变规范的插值不等式
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-27 DOI: 10.1007/s43036-024-00371-4
Ahmad Al-Natoor, Omar Hirzallah, Fuad Kittaneh
{"title":"Interpolating inequalities for unitarily invariant norms of matrices","authors":"Ahmad Al-Natoor,&nbsp;Omar Hirzallah,&nbsp;Fuad Kittaneh","doi":"10.1007/s43036-024-00371-4","DOIUrl":"10.1007/s43036-024-00371-4","url":null,"abstract":"<div><p>In this paper, we prove several interpolating inequalities for unitarily invariant norms of matrices. Using the log-convexity of certain functions, enables us to obtain refinements of recent norm inequalities. Generalizations of some well-known norm inequalities are also given.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141798216","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
Strong and weak estimates for some sublinear operators in Herz spaces with power weights at indices beyond critical index 赫兹空间中某些亚线性算子的强估计和弱估计，其指数超过临界指数时的幂权
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-27 DOI: 10.1007/s43036-024-00368-z
Katsuo Matsuoka
{"title":"Strong and weak estimates for some sublinear operators in Herz spaces with power weights at indices beyond critical index","authors":"Katsuo Matsuoka","doi":"10.1007/s43036-024-00368-z","DOIUrl":"10.1007/s43036-024-00368-z","url":null,"abstract":"<div><p>In 1996, X. Li and D. Yang found the best possible range of index <span>(alpha )</span> for the boundedness of some sublinear operators on Herz spaces <span>({dot{K}}_q^{alpha , p}({{mathbb {R}}}^n))</span> or <span>(K_q^{alpha , p}({{mathbb {R}}}^n))</span>, under a certain size condition. Also, in 1994 and 1995, S. Lu and F. Soria showed that concerning the boundedness of above sublinear operator <i>T</i> on <span>({dot{K}}_q^{alpha , p}({{mathbb {R}}}^n))</span> or <span>(K_q^{alpha , p}({{mathbb {R}}}^n))</span> with critical index of <span>(alpha )</span>, <i>T</i> is bounded on the power-weighted Herz spaces <span>({dot{K}}_q^{alpha , p}(w)({{mathbb {R}}}^n))</span> or <span>(K_q^{alpha , p}(w)({{mathbb {R}}}^n))</span>. In this paper, we will prove that for the two-power-weighted Herz spaces <span>({dot{K}}_{q_1}^{alpha , p}(w_1,w_2)({{mathbb {R}}}^n))</span> or <span>(K_{q_2}^{alpha , p}(w_1,w_2)({{mathbb {R}}}^n))</span> with indices beyond critical index of <span>(alpha )</span>, the above <i>T</i> is bounded on them. Further, we will extend this result to a sublinear operator satisfying another size condition and a pair of Herz spaces <span>(K_q^{alpha , p}(w_{beta _1},w_{beta _2})({{mathbb {R}}}^n))</span> and <span>(K_q^{alpha , p}(w_{gamma _1},w_{gamma _2})({{mathbb {R}}}^n))</span>. Moreover, we will also show the result of weak version of the above boundedness.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141797445","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
Compactness of commutators of Hardy operators on Heisenberg group 海森堡群上哈代算子换元的紧凑性
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-25 DOI: 10.1007/s43036-024-00369-y
Jin Xu, Jiman Zhao
{"title":"Compactness of commutators of Hardy operators on Heisenberg group","authors":"Jin Xu,&nbsp;Jiman Zhao","doi":"10.1007/s43036-024-00369-y","DOIUrl":"10.1007/s43036-024-00369-y","url":null,"abstract":"<div><p>In this paper, we study the commutators of the Hardy operators on the Heisenberg group. We get some sufficient and necessary conditions for the compactness of the commutators of the Hardy operators on the Heisenberg group.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141803984","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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