Browsing by Author "Wong, Ngai-Ching"

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The spectrum of the product of operators, and the product of their numerical ranges
(2015-03-15)
Li, Chi-Kwong
;
Tsai, Ming-Cheng
;
Wang, Kuo-Zhong
;
Wong, Ngai-Ching
;
應用數學系
We show that a compact operator A is a multiple of a positive semi-definite operator if and only if sigma(AB) subset of <(W(A)W(B))over bar>, for 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. (C) 2014 Elsevier Inc. All rights reserved.