The bounded approximation property of variable Lebesgue spaces and nuclearity

2015/03/24 by Delgado, Julio, Ruzhansky, Michael
#46B28 #47B06 (Secondary) #47B10 (Primary) #47G10 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1503.07202

Abstract

In this paper we prove the bounded approximation property for variable exponent Lebesgue spaces, study the concept of nuclearity on such spaces and apply it to trace formulae such as the Grothendieck-Lidskii formula. We apply the obtained results to derive criteria for nuclearity and trace formulae for periodic operators on \mathbb Rⁿ in terms of global symbols.

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