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arXiv · 2210.05887

Non-rough norms and dentability in spaces of operators

Susmita Seal·Sudeshna Basu·Julio Becerra Guerrero·Juan Miguel Villegas Yeguas
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Abstract

In this work, we study non-rough norms in L(X,Y), the space of bounded linear operators between Banach spaces X and Y. We prove that L(X,Y) has non-rough norm if and only if X* and Y have non-rough norm. We show that the injective tensor product of X and Y has non-rough norm if and only if both X and Y have non-rough norm. We also give an example to show that non-rough norms are not stable under projective tensor product. We also study a related concept namely the small diameter properties in the context of L(X,Y)*. These results leads to a discussion on stability of the small diameter properties for projective and injective tensor product spaces.

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Susmita Seal, Sudeshna Basu, Julio Becerra Guerrero, Juan Miguel Villegas Yeguas. 2022-10-12. Non-rough norms and dentability in spaces of operators. https://arxiv.org/abs/2210.05887

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