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Remarks on a theorem of Taskinen on spaces of continuous functions

✍ Scribed by Ignacio Villanueva

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 145 KB
Volume: 250
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310024

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✦ Synopsis

Abstract

We clarify and prove in a simpler way a result of Taskinen about symmetric operators on C(K^n^), K an uncountable metrizable compact space. To do this we prove that, for any compact space K and any n ∈ ℕ, the symmetric injective n–tensor product of C(K), $ \widehat {\bigotimes} ^n _{s, \epsilon} C(K) $, is complemented in C(B~C(K)*~), a result of independent interest. The techniques we develop allow us to extend the result in several directions. We also show that the hypothesis of metrizability and uncountability cannot be removed.

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