Power type asymptotically uniformly smooth and asymptotically uniformly flat norms
Copyright policy )Power type asymptotically uniformly smooth and asymptotically uniformly flat norms
We provide a short characterization of $p$-asymptotic uniform smoothability and asymptotic uniform flatenability of operators and of Banach spaces. We use these characterizations to show that many asymptotic uniform smoothness properties pass to injective tensor products of operators and of Banach spaces. In particular, we prove that the injective tensor product of two asymptotically uniformly smooth Banach spaces is asymptotically uniformly smooth. We prove that for $1
- Miami University United States
- University System of Ohio United States
- MIAMI UNIVERSITY
- Department of Mathematics
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Operator ideals, Mathematics - Functional Analysis, Asymptotic theory of Banach spaces, ordinal ranks, FOS: Mathematics, Spaces of operators; tensor products; approximation properties, Szlenk index, operator ideals, Functional Analysis (math.FA)
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Operator ideals, Mathematics - Functional Analysis, Asymptotic theory of Banach spaces, ordinal ranks, FOS: Mathematics, Spaces of operators; tensor products; approximation properties, Szlenk index, operator ideals, Functional Analysis (math.FA)
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