Research Article Schur Algebras over C -Algebras
نویسندگان
چکیده
Let be a C∗-algebra with identity 1, and let s( ) denote the set of all states on . For p,q,r ∈ [1,∞), denote by r( ) the set of all infinite matrices A= [ajk]j,k=1 over such that the matrix (φ[A[2]]) [r] := [(φ(ajkajk))]j,k=1 defines a bounded linear operator from p to q for all φ∈ s( ). Then r( ) is a Banach algebra with the Schur product operation and norm ‖A‖ = sup{‖(φ[A[2]])‖ : φ∈ s( )}. 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.
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