Lifshitz-Krein trace formula for Hirsch functiuonal calculus on Banach spaces

2018/05/03 by Mirotin, Adolf R
#47B10 #47L20 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A56 #Secondary 47A55

paper · doi:10.48550/arxiv.1805.01337

Abstract

We give a simple definition of a spectral shift function for pairs of nonpositive operators on Banach spaces and prove trace formulas of Lifshitz-Kre\uın type for a perturbation of an operator monotonic (negative complete Bernstein) function of negative and nonpositive operators on Banach spaces induced by nuclear perturbation of an operator argument. The Lipschitzness of such functions is also investigated. The results may be regarded as a contribution to a perturbation theory for Hirsch functional calculus.

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