On Bounded Finite Potent Operators on arbitrary Hilbert Spaces

2021/03/06 by Fernando Pablos Romo, Romo, Fernando Pablos
Mathematics · #46C05 #47A05 #47L30 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46C05 #msc:47A05 #msc:47L30

paper · pdf · doi:10.48550/arxiv.2103.04089

19 pages

arxiv created 2021/03/06 · arxiv updated 2021/03/09

Abstract

The aim of this work is to study the structure of bounded finite potent endomorphisms on Hilbert spaces. In particular, for these operators, an answer to the Invariant Subspace Problem is given and the main properties of its adjoint operator are offered. Moreover, for every bounded finite potent endomorphism we show that Tate's trace coincides with the Leray trace and with the trace defined by R. Elliott for Riesz Trace Class operators.

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