An \(n\times n\) matrix of linear functionals of \(C^{*}\)-algebras (Q1608156)
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scientific article; zbMATH DE number 1779097
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An \(n\times n\) matrix of linear functionals of \(C^{*}\)-algebras |
scientific article; zbMATH DE number 1779097 |
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An \(n\times n\) matrix of linear functionals of \(C^{*}\)-algebras (English)
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12 August 2002
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Summary: We show that any bounded matrix of linear functionals \([ f_{ ij}]:M_{n} (A)\to M_{n} ({\mathbb C})\) has a representation \(f_{ ij} (a)=\langle T\pi (a)x_{j},x_{i}\rangle\), \(a\in A\), \(i,j=1,2,\dots,n\), for some representation \(\pi\) on a Hilbert space \(K\) and an \(n\) vectors \(x _{1,}x_{2},\dots,x_{n}\) in \(K\).
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bounded matrix of linear functionals
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representation
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