Operator equations and subscalarity
- 주제(키워드) Bishop's property (β) , Invariant subspace , Subscalar
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Instytut Matematyczny
- 발행년도 2014
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000114235
- 본문언어 영어
- Published As http://dx.doi.org/10.4064/sm225-2-1
초록/요약
We consider the system of operator equations ABA = A2 and BAB = B2. Let (A, B) be a solution to this system. We give several connections among the operators A, B, AB, and BA. We first prove that A is subscalar of finite order if and only if B is, which is equivalent to the subscalarity of AB or BA with finite order. As a corollary, if A is subscalar and its spectrum has nonempty interior, then B has a nontrivial invariant subspace. We also provide examples of subscalar operator matrices. Moreover, we deal with algebraicity, power boundedness, and quasitriangularity, using some power properties obtained from the operator equations.
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