Note on some operator equations and local spectral properties
- 주제(키워드) Operator equations , Single valued extension property , Spectrum
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Element D.O.O.
- 발행년도 2016
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000135423
- 본문언어 영어
- Published As http://dx.doi.org/10.7153/oam-10-22
초록/요약
In this paper we define Sk, j by the set of solutions (A,B) of the operator equations AkBj+1Ak = A2k+j and BkAj+1Bk = B2k+j. Then we observe the set Sk, j is increasing for all integers k ≥ 1 and j ≥ 0. Now let a pair (A,B) ∈ Sk, j ∩ Sj+1,k−1 for any integer k ≥ 1 and j ≥ 0. We show that if any one of the operators A, AB, BA, and B has Bishop’s property (β), then all others have the same property. Furthermore, we prove that the operators Ak+j, AkBj+1, Aj+1Bk, Bj+1Ak, BkAj+1 and Bk+j have the same spectra and spectral properties. Finally, we investigate their Weyl type theorems. © 2016, Element D.O.O. All Rights Reserved.
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