# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Direct sums of irreducible operators

### Tom 155 / 2003

Studia Mathematica 155 (2003), 37-49 MSC: 47A15, 47C15. DOI: 10.4064/sm155-1-3

#### Streszczenie

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 $T$.

#### Autorzy

• Jun Shen FangDepartment of Mathematics
Hebei University of Technology
Tianjin 300130, China
e-mail
• Chun-Lan JiangDepartment of Mathematics
Hebei Nomal University
Shijiazhuang 050016, China
e-mail
• Pei Yuan WuDepartment of Applied Mathematics
National Chiao Tung University
Hsinchu 300, Taiwan
e-mail

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