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.

Kategorie tematyczne

• 47A62: Equations involving linear operators, with operator unknowns
• 47B20: Subnormal operators, hyponormal operators, etc.

• 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