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The centralizer of
tensor products of Banach spaces (a function space
representation)
Ehrhard Behrends |
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Vol. 81 (1979), No. 2, 291–301
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Abstract |
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Let X, Y be real Banach spaces, X⊗𝜖Y their usual 𝜖-tensor product. We represent Z(X⊗𝜖Y ), the centralizer of X⊗𝜖Y , as a space of real-valued functions on a suitable compact Hausdorff space. As a corollary we obtain Wickstead’s result: Z(X⊗𝜖Y ) is the closure with respect to the strong operator topology of Z(X) ⊗ Z(Y ). In addition it is shown that Z(X⊗𝜖Y ) is in fact the uniform closure of Z(X) ⊗ Z(Y ) provided the norm topology and the strong operator topology coincide on the centralizers of X and Y . |
Mathematical Subject Classification 2000
Primary: 46M05
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Milestones
Received: 15 September 1977
Revised: 5 May 1978
Published: 1 April 1979
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Authors |
| Ehrhard Behrends | |
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