Rough norms in spaces of operators

2016/06/04 by Haller, Rainis, Langemets, Johann, Põldvere, Märt
#46B20 #46B22 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1606.01359

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 δ-average rough whenever X^∗ is δ-average rough and Y is alternatively octahedral. This allows us to give a unified improvement of two theorems by Becerra Guerrero, López-Pérez, and Rueda Zoca [J. Math. Anal. Appl. 427 (2015)].

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• Non-rough norms and dentability in spaces of operators
• Nonrough norms in spaces with small diameter
• Octahedral norms in spaces of operators
• Characterization of k-smooth operators between Banach spaces
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