Superreflexive tensor product spaces

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2025年2月8日

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Abraham Rueda Zoca

摘要

The aim of this note is to prove that, given two superreflexive Banach spaces X and Y, then $X\widehat{\otimes }_\pi Y$ $X {\hat{\otimes}}_{π} Y$ is superreflexive if and only if either X or Y is finite-dimensional. In a similar way, we prove that $X\widehat{\otimes }_\varepsilon Y$ $X {\hat{\otimes}}_{ε} Y$ is superreflexive if and only if either X or Y is finite-dimensional.