Publication: Schatten's theorems on functionally defined schur algebras
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Issued Date
2005-09-13
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ISSN
01611712
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2-s2.0-27944509232
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Mahidol University
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SCOPUS
Bibliographic Citation
International Journal of Mathematics and Mathematical Sciences. Vol.2005, No.14 (2005), 2175-2193
Suggested Citation
Pachara Chaisuriya, Sing Cheong Ong Schatten's theorems on functionally defined schur algebras. International Journal of Mathematics and Mathematical Sciences. Vol.2005, No.14 (2005), 2175-2193. doi:10.1155/IJMMS.2005.2175 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/16643
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Title
Schatten's theorems on functionally defined schur algebras
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Abstract
For each triple of positive numbers p, q, r ≥ 1 and each commutative C* -algebra ℬ with identity 1 and the set s(ℬ) of states on ℬ, the set ℓr (ℬ) of all matrices A = [ajk] over ℬ such that φ [A[r]]:= [φ( ajkr)] defines a bounded operator from ℓp to ℓq for all φ ε s(ℬ) is shown to be a Banach algebra under the Schur product operation, and the norm ∥A∥ = ∥ A ∥p,q,r = sup{∥φ[A[r]]∥1/r : φ ε s(ℬ)}. Schatten's theorems about the dual of the compact operators, the trace-class operators, and the decomposition of the dual of the algebra of all bounded operators on a Hilbert space are extended to the ℓr (ℬ) setting. Copyright © 2005 Hindawi Publishing Corporation.