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arXiv · 1403.4746

Some Thoughts on Approximation Properties

Oleg Reinov
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Abstract

We study some known approximation properties and introduce and investigate several new approximation properties, closely connected with different quasi-normed tensor products. These are the properties like the $AP_s$ or $AP_{(s,w)}$ for $s\in (0,1],$ which give us the possibility to identify the spaces of $s$-nuclear and $(s,w)$-nuclear operators with the corresponding tensor products (e.g., related to Lorentz sequence spaces). Some applications are given (in particular, we present not difficult proofs of the trace-formulas of Grothendieck-Lidskii type for several ideals of nuclear operators).

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Oleg Reinov. 2014-03-19. Some Thoughts on Approximation Properties. https://arxiv.org/abs/1403.4746

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