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arXiv · 2409.16286

New examples of strongly subdifferentiable projective tensor products

Abraham Rueda Zoca
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Abstract

We prove that the norm of $X\widehat{\otimes}_\pi Y$ is SSD if either $X=\ell_p(I)$ for $p>2$ and $Y$ is a finite-dimensional Banach space such that the modulus of convexity is of power type $q<p$ (e.g. if $Y^*$ is a subspace of $L_q$) or if $X=c_0(I)$ and $Y^*$ is any uniformly convex finite-dimensional Banach space. We also provide a characterisation of SSD elements of a projective tensor product which attain its projective norm in terms of a strengthening of the a local Bollob\'as property for bilinear mappings.

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Abraham Rueda Zoca. 2024-09-24. New examples of strongly subdifferentiable projective tensor products. https://arxiv.org/abs/2409.16286

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