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Remarks on a theorem of Taskinen on spaces of continuous functions
Author(s) -
Villanueva Ignacio
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310024
Subject(s) - mathematics , metrization theorem , uncountable set , tensor product , injective function , pure mathematics , space (punctuation) , locally compact space , product (mathematics) , discrete mathematics , separable space , mathematical analysis , countable set , geometry , linguistics , philosophy
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.