Operator equations and subscalarity

Sungeun Jung, and Eungil Ko. "Operator equations and subscalarity." Studia Mathematica 225.2 (2014): 97-113. <http://eudml.org/doc/285836>.

@article{SungeunJung2014,
abstract = {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.},
author = {Sungeun Jung, Eungil Ko},
journal = {Studia Mathematica},
keywords = {subscalar; Bishop’s property (); invariant subspace},
language = {eng},
number = {2},
pages = {97-113},
title = {Operator equations and subscalarity},
url = {http://eudml.org/doc/285836},
volume = {225},
year = {2014},
}

TY - JOUR
AU - Sungeun Jung
AU - Eungil Ko
TI - Operator equations and subscalarity
JO - Studia Mathematica
PY - 2014
VL - 225
IS - 2
SP - 97
EP - 113
AB - 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.
LA - eng
KW - subscalar; Bishop’s property (); invariant subspace
UR - http://eudml.org/doc/285836
ER -