The numerical range as a spectral set

2017/02/02 by Michel Crouzeix, Crouzeix, Michel, César Palencia +1
Mathematics · #47A25 #47A30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A25 #msc:47A30

paper · pdf · doi:10.48550/arxiv.1702.00668

8 pages

arxiv created 2017/02/02 · arxiv updated 2017/02/03

Abstract

It is shown that the numerical range of a linear operator operator in a Hilbert space is a (complete) (1+√2)-spectral set. The proof relies, among other things, in the behavior of the Cauchy transform of the conjugates of holomorphic functions.

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