Operator equations and subscalarity

• Autorzy: Sungeun Jung , Eungil Ko
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 225
• Numer: 2
• Strony: 97-113

Daty

wydano

2014

Twórcy

autor

Sungeun Jung

• Institute of Mathematical Sciences, Ewha Womans University, 120-750 Seoul, Korea

autor

Eungil Ko

• Department of Mathematics, Ewha Womans University, 120-750 Seoul, Korea

Identyfikatory

DOI

10.4064/sm225-2-1