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arXiv · 1606.01359

Rough norms in spaces of operators

Rainis Haller·Johann Langemets·Märt Põldvere
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Abstract

We investigate sufficient and necessary conditions for the space of bounded linear operators between two Banach spaces to be rough or average rough. Our main result is that $\mathcal L(X,Y)$ is $\delta$-average rough whenever $X^\ast$ is $\delta$-average rough and $Y$ is alternatively octahedral. This allows us to give a unified improvement of two theorems by Becerra Guerrero, L\'opez-P\'erez, and Rueda Zoca [J. Math. Anal. Appl. 427 (2015)].

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Rainis Haller, Johann Langemets, Märt Põldvere. 2016-06-04. Rough norms in spaces of operators. https://arxiv.org/abs/1606.01359

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