Direct sums of irreducible operators

• Autorzy: Jun Shen Fang , Chun-Lan Jiang , Pei Yuan Wu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47C15: Operators in C * - or von Neumann algebras
• 47A15: Invariant subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 1
• Strony: 37-49

Daty

wydano

2003

Twórcy

autor

Jun Shen Fang

• Department of Mathematics, Hebei University of Technology, Tianjin 300130, China

autor

Chun-Lan Jiang

• Department of Mathematics, Hebei Nomal University, Shijiazhuang 050016, China

autor

Pei Yuan Wu

• Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan

Identyfikatory

DOI

10.4064/sm155-1-3