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Dana P. Williams
Tensor products with bounded continuous functions
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| Published: |
April 18, 2003
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| Keywords: |
Tensor products, C*-algebras, Stone-Čech compactification, pseudocompact |
| Subject: |
Primary: 46L06; Secondary: 54D35, 54D20 |
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Abstract
We study the natural inclusions of Cb(X)⊗A into Cb(X,A) and
Cb(X,Cb(Y)) into Cb(X×Y). In particular, excepting
trivial cases, both these maps are isomorphisms only when X and
Y are pseudocompact. This implies a result of Glicksberg showing
that the Stone-Čech compactificiation β(X×Y) is
naturally identified with βX × βY if and only if X and
Y are pseudocompact.
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| Author information
Department of Mathematics, Bradley Hall, Dartmouth College, Hanover, NH 03755-3551, USA
dana.williams@dartmouth.edu
http://www.math.dartmouth.edu/~dana
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