Advances in Operator Theory最新文献_第6页

Endpoint estimates for commutators with respect to the fractional integral operators on Orlicz–Morrey spaces 关于奥利兹-莫雷空间上分数积分算子的换元器端点估计

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Advances in Operator Theory Pub Date : 2024-10-18 DOI: 10.1007/s43036-024-00379-w

Naoya Hatano

引用次数: 0

Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices 某些三重扰动一致矩阵列凸壳的效率

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Advances in Operator Theory Pub Date : 2024-10-14 DOI: 10.1007/s43036-024-00384-z

Susana Furtado, Charles Johnson

{"title":"Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices","authors":"Susana Furtado, Charles Johnson","doi":"10.1007/s43036-024-00384-z","DOIUrl":"10.1007/s43036-024-00384-z","url":null,"abstract":"<div>In decision making a weight vector is often obtained from a reciprocal matrix A that gives pairwise comparisons among n alternatives. The weight vector should be chosen from among efficient vectors for A. Since the reciprocal matrix is usually not consistent, there is no unique way of obtaining such a vector. It is known that all weighted geometric means of the columns of A are efficient for A. In particular, any column and the standard geometric mean of the columns are efficient, the latter being an often used weight vector. Here we focus on the study of the efficiency of the vectors in the (algebraic) convex hull of the columns of A. This set contains the (right) Perron eigenvector of A, a classical proposal for the weight vector, and the Perron eigenvector of (AA^{T}) (the right singular vector of A), recently proposed as an alternative. We consider reciprocal matrices A obtained from a consistent matrix C by modifying at most three pairs of reciprocal entries contained in a 4-by-4 principal submatrix of C. For such matrices, we give necessary and sufficient conditions for all vectors in the convex hull of the columns to be efficient. In particular, this generalizes the known sufficient conditions for the efficiency of the Perron vector. Numerical examples comparing the performance of efficient convex combinations of the columns and weighted geometric means of the columns are provided.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434920","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 c-numerical range of a quaternion skew-Hermitian matrix is convex 四元偏斜-赫米特矩阵的 c 数值范围是凸的

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Advances in Operator Theory Pub Date : 2024-10-14 DOI: 10.1007/s43036-024-00391-0

Alma van der Merwe, Madelein Thiersen, Hugo J. Woerdeman

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Correction to: g-Riesz Operators and Their Spectral Properties 更正：g-Riesz 算子及其谱特性

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Advances in Operator Theory Pub Date : 2024-10-14 DOI: 10.1007/s43036-024-00385-y

Abdelhalim Azzouz, Mahamed Beghdadi, Bilel Krichen

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On the Cesàro hypercyclic linear relations 关于塞萨罗超循环线性关系

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Advances in Operator Theory Pub Date : 2024-10-10 DOI: 10.1007/s43036-024-00387-w

Ali Ech-Chakouri, Hassane Zguitti

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Spectral theory for fractal pseudodifferential operators 分形伪微分算子的谱理论

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Advances in Operator Theory Pub Date : 2024-10-09 DOI: 10.1007/s43036-024-00381-2

Hans Triebel

{"title":"Spectral theory for fractal pseudodifferential operators","authors":"Hans Triebel","doi":"10.1007/s43036-024-00381-2","DOIUrl":"10.1007/s43036-024-00381-2","url":null,"abstract":"<div>The paper deals with the distribution of eigenvalues of the compact fractal pseudodifferential operator (T^mu _tau ), <div><div>$$begin{aligned} big ( T^mu _tau fbig )(x) = int _{{{mathbb {R}}}^n} e^{-ixxi } , tau (x,xi ) , big ( fmu big )^vee (xi ) , {mathrm d}xi , qquad xin {{mathbb {R}}}^n, end{aligned}$$</div></div>in suitable special Besov spaces (B^s_p ({{mathbb {R}}}^n) = B^s_{p,p} ({{mathbb {R}}}^n)), (s>0), (1<p<infty ). Here (tau (x,xi )) are the symbols of (smooth) pseudodifferential operators belonging to appropriate Hörmander classes (Psi ^sigma _{1, delta } ({{mathbb {R}}}^n)), (sigma <0), (0 le delta le 1) (including the exotic case (delta =1)) whereas (mu ) is the Hausdorff measure of a compact d–set (Gamma ) in ({{mathbb {R}}}^n), (0<d<n). This extends previous assertions for the positive-definite selfadjoint fractal differential operator ((textrm{id}- Delta )^{sigma /2} mu ) based on Hilbert space arguments in the context of suitable Sobolev spaces (H^s ({{mathbb {R}}}^n) = B^s_2 ({{mathbb {R}}}^n)). We collect the outcome in the Main Theorem below. Proofs are based on estimates for the entropy numbers of the compact trace operator <div><div>$$begin{aligned} textrm{tr},_mu : quad B^s_p ({{mathbb {R}}}^n) hookrightarrow L_p (Gamma , mu ), quad s>0, quad 1<p<infty . end{aligned}$$</div></div>We add at the end of the paper a few personal reminiscences illuminating the role of Pietsch in connection with the creation of approximation numbers and entropy numbers.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00381-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410823","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

Hyponormal measurable operators, affiliated to a semifinite von Neumann algebra 超常可测算子，隶属于半有限冯-诺依曼代数

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Advances in Operator Theory Pub Date : 2024-10-07 DOI: 10.1007/s43036-024-00388-9

Airat Bikchentaev

{"title":"Hyponormal measurable operators, affiliated to a semifinite von Neumann algebra","authors":"Airat Bikchentaev","doi":"10.1007/s43036-024-00388-9","DOIUrl":"10.1007/s43036-024-00388-9","url":null,"abstract":"<div>Let (mathcal {M}) be a von Neumann algebra of operators on a Hilbert space (mathcal {H}) and (tau ) be a faithful normal semifinite trace on (mathcal {M}), (S(mathcal {M}, tau )) be the ( ^*)-algebra of all (tau )-measurable operators. Assume that an operator (Tin S(mathcal {M}, tau )) is paranormal or ( ^*)-paranormal. If (T^n) is (tau )-compact for some (nin mathbb {N}) then T is (tau )-compact; if (T^n=0) for some (nin mathbb {N}) then (T=0); if (T^3=T) then (T=T^*); if (T^2in L_1(mathcal {M}, tau )) then (Tin L_2(mathcal {M}, tau )) and (Vert TVert _2^2=Vert T^2Vert _1). If an operator (Tin S(mathcal {M}, tau )) is hyponormal and (T^{*p}T^q) is (tau )-compact for some (p, q in mathbb {N}cup {0}), (p+q ge 1) then T is normal. If (Tin S(mathcal {M}, tau )) is p-hyponormal for some (0<ple 1) then the operator ((T^*T)^p-(TT^*)^p) cannot have the inverse in ( mathcal {M}). If an operator (Tin S(mathcal {M}, tau )) is hyponormal (or cohyponormal) and the operator (T^2) is Hermitian then T is normal.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410387","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 method of cyclic resolvents for quasi-convex functions and quasi-nonexpansive mappings 准凸函数和准无穷映射的循环解析子方法

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Advances in Operator Theory Pub Date : 2024-10-07 DOI: 10.1007/s43036-024-00390-1

Hadi Khatibzadeh, Maryam Moosavi

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Inequalities between s-numbers s 数之间的不等式

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Advances in Operator Theory Pub Date : 2024-10-05 DOI: 10.1007/s43036-024-00386-x

Mario Ullrich

引用次数: 0

Norm behavior of Jordan and bidiagonal matrices 约旦矩阵和对角线矩阵的规范行为