期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2005
卷号：2005
DOI：10.1155/IJMMS.2005.2175
出版社：Hindawi Publishing Corporation
摘要：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 𝒮r(ℬ) of all matrices A=[ajk] over ℬ such that ϕ[A[r]]:=[ϕ(|ajk|r)] defines a bounded operator from ℓp to
ℓq for all ϕ∈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∈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 𝒮r(ℬ) setting.
