The spectrum of the product of operators, and the product of their numerical ranges

2014/04/23 by Li, Chi-Kwong, Tsai, Ming-Cheng, Wang, Kuo-Zhong +1
#15A60 #47A10 #47A12 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1404.5822

Abstract

We show that a compact operator A is a multiple of a positive semi-definite operator if and only if σ(AB) ⊆ W(A)W(B), \quadfor all (rank one) operators B. An example of a normal operator is given to show that the equivalence conditions may fail in general. We then obtain conditions to identify other classes of operators A so that equivalence conditions hold.

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