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Advances in Operator Theory最新文献

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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
The Riemann surface of the inverse of Jackson’s q-exponential function 杰克逊 q 指数函数逆的黎曼曲面
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-23 DOI: 10.1007/s43036-024-00367-0
István Mező
{"title":"The Riemann surface of the inverse of Jackson’s q-exponential function","authors":"István Mező","doi":"10.1007/s43036-024-00367-0","DOIUrl":"10.1007/s43036-024-00367-0","url":null,"abstract":"<div><p>The <span>(exp _q(z))</span> function is the standard <i>q</i>-analogue of the exponential. Since not much is known about this function, our aim is to give a contribution to the knowledge on <span>(exp _q)</span>. After proving some simpler but new relations for it, we make a complete description of the inverse map of <span>(exp _q(z))</span>, including its branch structure and Riemann surface.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141812764","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 Brown–Halmos theorem for discrete Wiener–Hopf operators 离散维纳-霍普夫算子的布朗-哈尔莫斯定理
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-17 DOI: 10.1007/s43036-024-00370-5
Oleksiy Karlovych, Sandra Mary Thampi
{"title":"The Brown–Halmos theorem for discrete Wiener–Hopf operators","authors":"Oleksiy Karlovych,&nbsp;Sandra Mary Thampi","doi":"10.1007/s43036-024-00370-5","DOIUrl":"10.1007/s43036-024-00370-5","url":null,"abstract":"<div><p>We prove an analogue of the Brown–Halmos theorem for discrete Wiener–Hopf operators acting on separable rearrangement-invariant Banach sequence spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00370-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141831505","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
Weighted composition operators on variable exponent Lebesgue spaces 可变指数勒贝格空间上的加权合成算子
IF 0.8
Advances in Operator Theory Pub Date : 2024-07-13 DOI: 10.1007/s43036-024-00366-1
Gopal Datt, Daljeet Singh Bajaj, Alberto Fiorenza
{"title":"Weighted composition operators on variable exponent Lebesgue spaces","authors":"Gopal Datt,&nbsp;Daljeet Singh Bajaj,&nbsp;Alberto Fiorenza","doi":"10.1007/s43036-024-00366-1","DOIUrl":"10.1007/s43036-024-00366-1","url":null,"abstract":"<div><p>In this paper, we characterize the boundedness of weighted composition operators, induced by measurable transformations and complex-valued measurable functions, on variable exponent Lebesgue spaces. We also derive conditions for these operators to be compact or injective or have closed range. In addition, we investigate some relations between these operators and multiplication operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00366-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141698653","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
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