Some Thoughts on Approximation Properties

2014/03/19 by Reinov, Oleg
#46B28 Spaces of operators #FOS: Mathematics #Functional Analysis (math.FA) #approximation properties #tensor products

paper · doi:10.48550/arxiv.1403.4746

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∈ (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).

Related

• Approximation properties AP_s and p-nuclear operators (the case where 0<s≤ 1)
• Approximation property and nuclearity on mixed-norm L^p, modulation and Wiener amalgam spaces
• Norm-attaining tensors and nuclear operators
• Trace, determinant and eigenvalues of nuclear operators
• The bounded approximation property of variable Lebesgue spaces and nuclearity