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Generalized Crofoot transform and applications 广义Crofoot变换及其应用
IF 0.6
Concrete Operators Pub Date : 2023-01-01 DOI: 10.1515/conop-2022-0138
Rewayat Khan, A. Farooq
{"title":"Generalized Crofoot transform and applications","authors":"Rewayat Khan, A. Farooq","doi":"10.1515/conop-2022-0138","DOIUrl":"https://doi.org/10.1515/conop-2022-0138","url":null,"abstract":"Abstract Matrix-valued asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These are the generalization of matrix-valued truncated Toeplitz operators. In this article, we describe symbols of matrix-valued asymmetric truncated Toeplitz operators equal to the zero operator. We also use generalized Crofoot transform to find a connection between the symbols of matrix-valued asymmetric truncated Toeplitz operators T ( Θ 1 , Θ 2 ) {mathcal{T}}left({Theta }_{1},{Theta }_{2}) and T ( Θ 1 ′ , Θ 2 ′ ) {mathcal{T}}left({Theta }_{1}^{^{prime} },{Theta }_{2}^{^{prime} }) .","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45662702","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: 1
On the compactness and the essential norm of operators defined by infinite tridiagonal matrices 关于无穷三对角矩阵定义算子的紧致性和本质范数
IF 0.6
Concrete Operators Pub Date : 2023-01-01 DOI: 10.1515/conop-2022-0143
Alexander Caicedo, J. Ramos-Fernández, M. Salas-Brown
{"title":"On the compactness and the essential norm of operators defined by infinite tridiagonal matrices","authors":"Alexander Caicedo, J. Ramos-Fernández, M. Salas-Brown","doi":"10.1515/conop-2022-0143","DOIUrl":"https://doi.org/10.1515/conop-2022-0143","url":null,"abstract":"Abstract In this article, all sequences u {boldsymbol{u}} , v {boldsymbol{v}} , and w {boldsymbol{w}} that define continuous and compact tridiagonal operators T u , v , w {T}_{u,v,w} acting on the weighted sequence space l β 2 {l}_{beta }^{2} were characterized. Additionally, the essential norm of this operator, and as an important consequence of our results, the essential norm of multiplication operator M u {M}_{u} acting on l β 2 {l}_{beta }^{2} spaces was calculated.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41670534","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 Hausdorff operator on Bergmann spaces Bergmann空间上的广义Hausdorff算子
Concrete Operators Pub Date : 2023-01-01 DOI: 10.1515/conop-2023-0101
Sasikala Perumal, Kalaivani Kamalakkannan
{"title":"Generalized Hausdorff operator on Bergmann spaces","authors":"Sasikala Perumal, Kalaivani Kamalakkannan","doi":"10.1515/conop-2023-0101","DOIUrl":"https://doi.org/10.1515/conop-2023-0101","url":null,"abstract":"Abstract In this article, we considered the generalized Hausdorff operator <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">ℋ</m:mi> </m:mrow> <m:mrow> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi>ϕ</m:mi> <m:mo>,</m:mo> <m:mi>a</m:mi> </m:mrow> </m:msub> </m:math> {{mathcal{ {mathcal H} }}}_{mu ,phi ,a} on Bergmann space and determined the conditions on <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>ϕ</m:mi> </m:math> phi and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>a</m:mi> </m:math> a so that the operator is bounded. In addition, we studied the action of the Hausdorff operator on the truncated domain to estimate norm <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">ℋ</m:mi> </m:mrow> <m:mrow> <m:mi>μ</m:mi> <m:mo>,</m:mo> <m:mi>ϕ</m:mi> <m:mo>,</m:mo> <m:mi>a</m:mi> </m:mrow> </m:msub> </m:math> {{mathcal{ {mathcal H} }}}_{mu ,phi ,a} and established a relation with quasi-Hausdorff operator on Bergmann space.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135705256","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
Estimation of coefficient bounds for a subclass of Sakaguchi kind functions mapped onto various domains 映射到不同域上的Sakaguchi类函数子类的系数界估计
IF 0.6
Concrete Operators Pub Date : 2023-01-01 DOI: 10.1515/conop-2022-0140
B. Aarthy, B. Keerthi
{"title":"Estimation of coefficient bounds for a subclass of Sakaguchi kind functions mapped onto various domains","authors":"B. Aarthy, B. Keerthi","doi":"10.1515/conop-2022-0140","DOIUrl":"https://doi.org/10.1515/conop-2022-0140","url":null,"abstract":"Abstract In this article, we define a new subclass of analytic functions ℛ ( t , δ ) {mathcal{ {mathcal R} }}left(t,delta ) in the open unit disk D {mathbb{D}} associated with the petal-shaped domain. The bounds of the coefficients a 2 {a}_{2} , a 3 {a}_{3} , and a 4 {a}_{4} for the functions in the new class are obtained. We also acquire the bound of the Fekete-Szegö inequality and the bound of the Toeplitz determinants T 2 ( 2 ) {{mathcal{T}}}_{2}left(2) and T 3 ( 1 ) {{mathcal{T}}}_{3}left(1) for the functions in the defined class.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45305020","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
m-Isometric tensor products m等轴张量积
IF 0.6
Concrete Operators Pub Date : 2023-01-01 DOI: 10.1515/conop-2022-0142
Bhagawati Prashad Duggal, I. Kim
{"title":"m-Isometric tensor products","authors":"Bhagawati Prashad Duggal, I. Kim","doi":"10.1515/conop-2022-0142","DOIUrl":"https://doi.org/10.1515/conop-2022-0142","url":null,"abstract":"Abstract Given Banach space operators S i {S}_{i} and T i {T}_{i} , i = 1 , 2 i=1,2 , we use elementary properties of the left and right multiplication operators to prove, that if the tensor products pair ( S 1 ⊗ S 2 , T 1 ⊗ T 2 ) left({S}_{1}otimes {S}_{2},{T}_{1}otimes {T}_{2}) is strictly m m -isometric, i.e., Δ S 1 ⊗ S 2 , T 1 ⊗ T 2 m ( I ⊗ I ) = ∑ j = 0 m ( − 1 ) j m j ( S 1 ⊗ S 2 ) m − j ( T 1 ⊗ T 2 ) m − j = 0 {Delta }_{{S}_{1}otimes {S}_{2},{T}_{1}otimes {T}_{2}}^{m}left(Iotimes I)={sum }_{j=0}^{m}{left(-1)}^{j}left(begin{array}{c}m jend{array}right){left({S}_{1}otimes {S}_{2})}^{m-j}{left({T}_{1}otimes {T}_{2})}^{m-j}=0 , then there exist a non-zero scalar c c and positive integers m 1 , m 2 ≤ m {m}_{1},{m}_{2}le m such that m = m 1 + m 2 − 1 m={m}_{1}+{m}_{2}-1 , ( S 1 , c T 1 ) left({S}_{1},c{T}_{1}) is strict- m 1 {m}_{1} -isometric and S 2 , 1 c T 2 left({S}_{2},frac{1}{c}{T}_{2}right) is strict m 2 {m}_{2} -isometric.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41973409","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
Eigenvalue asymptotics for a class of multi-variable Hankel matrices 一类多变量汉克尔矩阵的特征值渐近性
IF 0.6
Concrete Operators Pub Date : 2022-06-25 DOI: 10.1515/conop-2022-0137
Christos Panagiotis Tantalakis
{"title":"Eigenvalue asymptotics for a class of multi-variable Hankel matrices","authors":"Christos Panagiotis Tantalakis","doi":"10.1515/conop-2022-0137","DOIUrl":"https://doi.org/10.1515/conop-2022-0137","url":null,"abstract":"Abstract A one-variable Hankel matrix H a {H}_{a} is an infinite matrix H a = [ a ( i + j ) ] i , j ≥ 0 {H}_{a}={left[aleft(i+j)]}_{i,jge 0} . Similarly, for any d ≥ 2 dge 2 , a d d -variable Hankel matrix is defined as H a = [ a ( i + j ) ] {H}_{{bf{a}}}=left[{bf{a}}left({bf{i}}+{bf{j}})] , where i = ( i 1 , … , i d ) {bf{i}}=left({i}_{1},ldots ,{i}_{d}) and j = ( j 1 , … , j d ) {bf{j}}=left({j}_{1},ldots ,{j}_{d}) , with i 1 , … , i d , j 1 , … , j d ≥ 0 {i}_{1},ldots ,{i}_{d},{j}_{1},ldots ,{j}_{d}ge 0 . For γ > 0 gamma gt 0 , Pushnitski and Yafaev proved that the eigenvalues of the compact one-variable Hankel matrices H a {H}_{a} with a ( j ) = j − 1 ( log j ) − γ aleft(j)={j}^{-1}{left(log j)}^{-gamma } , for j ≥ 2 jge 2 , obey the asymptotics λ n ( H a ) ∼ C γ n − γ {lambda }_{n}left({H}_{a})hspace{0.33em} sim hspace{0.33em}{C}_{gamma }{n}^{-gamma } , as n → + ∞ nto +infty , where the constant C γ {C}_{gamma } is calculated explicitly. This article presents the following d d -variable analogue. Let γ > 0 gamma gt 0 and a ( j ) = j − d ( log j ) − γ aleft(j)={j}^{-d}{left(log j)}^{-gamma } , for j ≥ 2 jge 2 . If a ( j 1 , … , j d ) = a ( j 1 + ⋯ + j d ) {bf{a}}left({j}_{1},ldots ,{j}_{d})=aleft({j}_{1}+cdots +{j}_{d}) , then H a {H}_{{bf{a}}} is compact and its eigenvalues follow the asymptotics λ n ( H a ) ∼ C d , γ n − γ {lambda }_{n}left({H}_{{bf{a}}})hspace{0.33em} sim hspace{0.33em}{C}_{d,gamma }{n}^{-gamma } , as n → + ∞ nto +infty , where the constant C d , γ {C}_{d,gamma } is calculated explicitly.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45005453","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 essential spectrum, norm, and spectral radius of abstract multiplication operators 抽象乘法算子的基本谱、范数和谱半径
IF 0.6
Concrete Operators Pub Date : 2022-04-08 DOI: 10.1515/conop-2022-0141
A. R. Schep
{"title":"The essential spectrum, norm, and spectral radius of abstract multiplication operators","authors":"A. R. Schep","doi":"10.1515/conop-2022-0141","DOIUrl":"https://doi.org/10.1515/conop-2022-0141","url":null,"abstract":"Abstract Let E E be a complex Banach lattice and T T is an operator in the center Z ( E ) = { T : ∣ T ∣ ≤ λ I for some λ } Zleft(E)=left{T:| T| le lambda Ihspace{0.33em}hspace{0.1em}text{for some}hspace{0.1em}hspace{0.33em}lambda right} of E E . Then, the essential norm ‖ T ‖ e Vert T{Vert }_{e} of T T equals the essential spectral radius r e ( T ) {r}_{e}left(T) of T T . We also prove r e ( T ) = max { ‖ T A d ‖ , r e ( T A ) } {r}_{e}left(T)=max left{Vert {T}_{}hspace{-0.35em}{}_{{A}^{d}}Vert ,{r}_{e}left({T}_{A})right} , where T A {T}_{A} is the atomic part of T T and T A d {T}_{}hspace{-0.35em}{}_{{A}^{d}} is the nonatomic part of T T . Moreover, r e ( T A ) = limsup ℱ λ a {r}_{e}left({T}_{A})={mathrm{limsup}}_{{mathcal{ {mathcal F} }}}{lambda }_{a} , where ℱ {mathcal{ {mathcal F} }} is the Fréchet filter on the set A A of all positive atoms in E E of norm one and λ a {lambda }_{a} is given by T A a = λ a a {T}_{A}a={lambda }_{a}a for all a ∈ A ain A .","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43629578","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: 1
Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces L2空间中密定义复合算子的特定有界积的正态性和拟不规则性
IF 0.6
Concrete Operators Pub Date : 2022-01-01 DOI: 10.1515/conop-2022-0130
Hang Zhou
{"title":"Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces","authors":"Hang Zhou","doi":"10.1515/conop-2022-0130","DOIUrl":"https://doi.org/10.1515/conop-2022-0130","url":null,"abstract":"Abstract Let (X, 𝒜, μ) be a σ−finite measure space. A transformation ϕ : X → X is non-singular if μ ∘ ϕ−1 is absolutely continuous with respect with μ. For this non-singular transformation, the composition operator Cϕ: 𝒟(Cϕ) → L2(μ) is defined by Cϕf = f ∘ ϕ, f ∈ 𝒟(Cϕ). For a fixed positive integer n ≥ 2, basic properties of product Cϕn · · · Cϕ1 in L2(μ) are presented in Section 2, including the boundedness and adjoint. Under the assistance of these properties, normality and quasinormality of specific bounded Cϕn · · · Cϕ1 in L2(μ) are characterized in Section 3 and 4 respectively, where Cϕ1, Cϕ2, · · ·, Cϕn are all densely defined.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"9 1","pages":"86 - 95"},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41909001","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
Weighted composition operators on Hardy–Smirnov spaces Hardy–Smirnov空间上的加权复合算子
IF 0.6
Concrete Operators Pub Date : 2022-01-01 DOI: 10.1515/conop-2022-0136
Valentin Matache
{"title":"Weighted composition operators on Hardy–Smirnov spaces","authors":"Valentin Matache","doi":"10.1515/conop-2022-0136","DOIUrl":"https://doi.org/10.1515/conop-2022-0136","url":null,"abstract":"Abstract Operators of type f → ψf ◦ φ acting on function spaces are called weighted composition operators. If the weight function ψ is the constant function 1, then they are called composition operators. We consider weighted composition operators acting on Hardy–Smirnov spaces and prove that their unitarily invariant properties are reducible to the study of weighted composition operators on the classical Hardy space over a disc. We give examples of such results, for instance proving that Forelli’s theorem saying that the isometries of non–Hilbert Hardy spaces over the unit disc need to be special weighted composition operators extends to all non–Hilbert Hardy–Smirnov spaces. A thorough study of boundedness of weighted composition operators is performed.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"9 1","pages":"160 - 176"},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47454508","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 unitary equivalence to a self-adjoint or doubly–positive Hankel operator 关于自伴随或双正Hankel算子的幺正等价
IF 0.6
Concrete Operators Pub Date : 2022-01-01 DOI: 10.1515/conop-2022-0132
R.T.W. Martin
{"title":"On unitary equivalence to a self-adjoint or doubly–positive Hankel operator","authors":"R.T.W. Martin","doi":"10.1515/conop-2022-0132","DOIUrl":"https://doi.org/10.1515/conop-2022-0132","url":null,"abstract":"Abstract Let A be a bounded, injective and self-adjoint linear operator on a complex separable Hilbert space. We prove that there is a pure isometry, V, so that AV > 0 and A is Hankel with respect to V, i.e. V*A = AV, if and only if A is not invertible. The isometry V can be chosen to be isomorphic to N ∈ ℕ ∪ {+∞} copies of the unilateral shift if A has spectral multiplicity at most N. We further show that the set of all isometries, V, so that A is Hankel with respect to V, are in bijection with the set of all closed, symmetric restrictions of A−1.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"9 1","pages":"114 - 126"},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43526464","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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