New York Journal of Mathematics
Volume 9 (2003) 69-77


Dana P. Williams

Tensor products with bounded continuous functions

Published: April 18, 2003
Keywords: Tensor products, C*-algebras, Stone-Čech compactification, pseudocompact
Subject: Primary: 46L06; Secondary: 54D35, 54D20

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.

Author information

Department of Mathematics, Bradley Hall, Dartmouth College, Hanover, NH 03755-3551, USA