Browsing by Author "Tsai, Ming-Cheng"

Now showing 1 - 2 of 2

Product of operators and numerical range
(2016-01-02)
Chien, Mao-Ting
;
Gau, Hwa-Long
;
Li, Chi-Kwong
;
Tsai, Ming-Cheng
;
Wang, Kuo-Zhong
We show that a bounded linear operator A is an element of B(H) is a multiple of a unitary operator if and only if AZ and Z A always have the same numerical radius or the same numerical range for all (rank one) Z is an element of B(H). More generally, for any bounded linear operators A, B is an element of B(H), we show that AZ and ZB always have the same numerical radius (resp., the same numerical range) for all (rank one) Z is an element of B(H) if and only if A = e(it) B (resp., A = B) is a multiple of a unitary operator for some t is an element of [0, 2 pi). We extend the result to other types of generalized numerical ranges including the k-numerical range and the higher rank numerical range.
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.