Restriction of Uniform Crossnorms

Carlos S. Kubrusly

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arXiv · 2212.10780

Restriction of Uniform Crossnorms

Carlos S. Kubrusly

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Abstract

Consider the space $B[X\otimes_αY]$ of operators on the tensors product ${X\otimes_αY}$ of normed spaces $X$ and $Y$ equipped with a uniform crossnorm ${\|\cdot\|_α}$$.$ Take the induced uniform norm on $B[X\otimes_αY]$ and consider its restriction to the tensor product ${B[X]\otimes B[Y]}$ of the algebra of operators $B[X]$ and $B[Y].$ It is proved that such a restriction is a reasonable crossnorm on ${B[X]\otimes B[Y]}$.

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BibTeX RIS

Carlos S. Kubrusly. 2023-02-03. Restriction of Uniform Crossnorms. https://arxiv.org/abs/2212.10780

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