Schur Algebras over C*-Algebras
Let 𝒜 be a C*-algebra with identity 1, and let s(𝒜) denote the set of all states on 𝒜. For p,q,r∈[1,∞), denote by 𝒮r(𝒜) the set of all infinite matrices A=[ajk]j,k=1∞ over 𝒜 such that the matrix (ϕ[A[2]])[r]:=[(ϕ(ajk*ajk))r]j,...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/63808 |
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| author | Pachara Chaisuriya Sing-Cheong Ong Sheng-Wang Wang |
| author_facet | Pachara Chaisuriya Sing-Cheong Ong Sheng-Wang Wang |
| author_sort | Pachara Chaisuriya |
| collection | DOAJ |
| description | Let 𝒜 be a C*-algebra with identity 1, and let s(𝒜)
denote the set of all states on 𝒜. For p,q,r∈[1,∞), denote by 𝒮r(𝒜) the set of all infinite matrices A=[ajk]j,k=1∞ over 𝒜 such that the matrix (ϕ[A[2]])[r]:=[(ϕ(ajk*ajk))r]j,k=1∞ defines a bounded linear operator from ℓp to ℓq for all ϕ∈s(𝒜). Then 𝒮r(𝒜) is a Banach algebra with the Schur product operation and norm
‖A‖=sup{‖(ϕ[A[2]])r‖1/(2r):ϕ∈s(𝒜)}. Analogs of Schatten's theorems on dualities among the compact
operators, the trace-class operators, and all the bounded operators on
a Hilbert space are proved. |
| format | Article |
| id | doaj-art-ee6848dc1d034a69bff053c7f7557d14 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ee6848dc1d034a69bff053c7f7557d142025-02-03T06:48:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/6380863808Schur Algebras over C*-AlgebrasPachara Chaisuriya0Sing-Cheong Ong1Sheng-Wang Wang2Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10700, ThailandDepartment of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USADepartment of Mathematics, Nanjing University, Nanjing 210029, ChinaLet 𝒜 be a C*-algebra with identity 1, and let s(𝒜) denote the set of all states on 𝒜. For p,q,r∈[1,∞), denote by 𝒮r(𝒜) the set of all infinite matrices A=[ajk]j,k=1∞ over 𝒜 such that the matrix (ϕ[A[2]])[r]:=[(ϕ(ajk*ajk))r]j,k=1∞ defines a bounded linear operator from ℓp to ℓq for all ϕ∈s(𝒜). Then 𝒮r(𝒜) is a Banach algebra with the Schur product operation and norm ‖A‖=sup{‖(ϕ[A[2]])r‖1/(2r):ϕ∈s(𝒜)}. Analogs of Schatten's theorems on dualities among the compact operators, the trace-class operators, and all the bounded operators on a Hilbert space are proved.http://dx.doi.org/10.1155/2007/63808 |
| spellingShingle | Pachara Chaisuriya Sing-Cheong Ong Sheng-Wang Wang Schur Algebras over C*-Algebras International Journal of Mathematics and Mathematical Sciences |
| title | Schur Algebras over C*-Algebras |
| title_full | Schur Algebras over C*-Algebras |
| title_fullStr | Schur Algebras over C*-Algebras |
| title_full_unstemmed | Schur Algebras over C*-Algebras |
| title_short | Schur Algebras over C*-Algebras |
| title_sort | schur algebras over c algebras |
| url | http://dx.doi.org/10.1155/2007/63808 |
| work_keys_str_mv | AT pacharachaisuriya schuralgebrasovercalgebras AT singcheongong schuralgebrasovercalgebras AT shengwangwang schuralgebrasovercalgebras |