홈 editorial content online
Volume 14 (2012)
No 1
Volume 13 (2011)
No 1
Volume 12 (2010)
No 1
Volume 11 (2009)
No 1, No 2
Volume 10 (2008)
No 1, No 2
Volume 9 (2006)
No 1, No 2
Volume 8 (2005)
No 1, No 2
Volume 7 (2004)
No 1, No 2
Volume 6 (2003)
No 1, No 2
Volume 5 (2002)
No 1, No 2
Volume 4 (2001)
No 1, No 2
Volume 3 (2000)
No 1
Volume 2 (1999)
No 1
Volume 1 (1998)
No 1

(1999 / vol.2 / no.1)
Direct Sums of Irreducible Operators
Jun Shen Fang, Chun-Lan Jiang, Pei Yuan Wu
Pages. 40-44     



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 unitary 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 $T$.



1. Introduction
2. Number of reducing subspaces
3. Full matrix algebras
4. Acknowledgements



Irreducible operator, reducing subspace, von Neumann algebra



47A15, 47C15