标题：Schur Algebras over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:math>-Algebras
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：2007
卷号：2007
DOI：10.1155/2007/63808
出版社：Hindawi Publishing Corporation
摘要：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.
