k-smoothness on polyhedral Banach spaces

2020/11/11 by Dey, Subhrajit, Mal, Arpita, Paul, Kallol · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B20 #Secondary 47L05

paper · doi:10.48550/arxiv.2011.05835

Abstract

We characterize k-smoothness of an element on the unit sphere of a finite-dimensional polyhedral Banach space. Then we study k-smoothness of an operator T ∈ \mathbbL(ℓ_∞ⁿ,\mathbbY), where \mathbbY is a two-dimensional Banach space with the additional condition that T attains norm at each extreme point of B_ℓ_∞ⁿ. We also characterize k-smoothness of an operator defined between ℓ_∞³ and ℓ₁³.

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