Direct sums of irreducible operators

Jun Shen Fang, Chun-Lan Jiang, and Pei Yuan Wu. "Direct sums of irreducible operators." Studia Mathematica 155.1 (2003): 37-49. <http://eudml.org/doc/284419>.

@article{JunShenFang2003,
abstract = {It is known that every operator on a (separable) Hilbert space is the direct integral of irreducible operators, but not every one is the direct sum of irreducible ones. We show that an operator can have either finitely or uncountably many reducing subspaces, and the former holds if and only if the operator is the direct sum of finitely many irreducible operators no two of which are unitarily equivalent. We also characterize operators T which are direct sums of irreducible operators in terms of the C*-structure of the commutant of the von Neumann algebra generated by T.},
author = {Jun Shen Fang, Chun-Lan Jiang, Pei Yuan Wu},
journal = {Studia Mathematica},
keywords = {irreducible operator; reducing subspace; von Neumann algebra},
language = {eng},
number = {1},
pages = {37-49},
title = {Direct sums of irreducible operators},
url = {http://eudml.org/doc/284419},
volume = {155},
year = {2003},
}

TY - JOUR
AU - Jun Shen Fang
AU - Chun-Lan Jiang
AU - Pei Yuan Wu
TI - Direct sums of irreducible operators
JO - Studia Mathematica
PY - 2003
VL - 155
IS - 1
SP - 37
EP - 49
AB - It is known that every operator on a (separable) Hilbert space is the direct integral of irreducible operators, but not every one is the direct sum of irreducible ones. We show that an operator can have either finitely or uncountably many reducing subspaces, and the former holds if and only if the operator is the direct sum of finitely many irreducible operators no two of which are unitarily equivalent. We also characterize operators T which are direct sums of irreducible operators in terms of the C*-structure of the commutant of the von Neumann algebra generated by T.
LA - eng
KW - irreducible operator; reducing subspace; von Neumann algebra
UR - http://eudml.org/doc/284419
ER -