Simultaneous solutions of operator Sylvester equations

Sang-Gu Lee, and Quoc-Phong Vu. "Simultaneous solutions of operator Sylvester equations." Studia Mathematica 222.1 (2014): 87-96. <http://eudml.org/doc/285507>.

@article{Sang2014,
abstract = {We consider simultaneous solutions of operator Sylvester equations $A_\{i\}X - XB_\{i\} = C_\{i\}$ (1 ≤ i ≤ k), where $(A₁,..., A_\{k\})$ and $(B₁,..., B_\{k\})$ are commuting k-tuples of bounded linear operators on Banach spaces and ℱ, respectively, and $(C₁,..., C_\{k\})$ is a (compatible) k-tuple of bounded linear operators from ℱ to , and prove that if the joint Taylor spectra of $(A₁,..., A_\{k\})$ and $(B₁,..., B_\{k\})$ do not intersect, then this system of Sylvester equations has a unique simultaneous solution.},
author = {Sang-Gu Lee, Quoc-Phong Vu},
journal = {Studia Mathematica},
keywords = {Sylvester equation; idempotent theorem; commutant; bicommutant; joint spectrum},
language = {eng},
number = {1},
pages = {87-96},
title = {Simultaneous solutions of operator Sylvester equations},
url = {http://eudml.org/doc/285507},
volume = {222},
year = {2014},
}

TY - JOUR
AU - Sang-Gu Lee
AU - Quoc-Phong Vu
TI - Simultaneous solutions of operator Sylvester equations
JO - Studia Mathematica
PY - 2014
VL - 222
IS - 1
SP - 87
EP - 96
AB - We consider simultaneous solutions of operator Sylvester equations $A_{i}X - XB_{i} = C_{i}$ (1 ≤ i ≤ k), where $(A₁,..., A_{k})$ and $(B₁,..., B_{k})$ are commuting k-tuples of bounded linear operators on Banach spaces and ℱ, respectively, and $(C₁,..., C_{k})$ is a (compatible) k-tuple of bounded linear operators from ℱ to , and prove that if the joint Taylor spectra of $(A₁,..., A_{k})$ and $(B₁,..., B_{k})$ do not intersect, then this system of Sylvester equations has a unique simultaneous solution.
LA - eng
KW - Sylvester equation; idempotent theorem; commutant; bicommutant; joint spectrum
UR - http://eudml.org/doc/285507
ER -