Invariant subspaces for finite maximal subdiagonal algebras

Kichi-Suke Saito

Vol. 93 (1981), No. 2, 431–434

DOI: 10.2140/pjm.1981.93.431

Abstract

Let M be a von Neumann algebra with a faithful, normal, tracial state τ and H^∞ a finite, maximal, subdiagonal algebra in M. If 1 ≦ p < s ≦∞, then there is a one-to-one correspondence between left-(resp. right-) invariant subspaces of the noncommutative Lebesgue space L^p(M,τ) and those of L^s(M,τ).

Mathematical Subject Classification 2000

Primary: 46L50, 46L50

Secondary: 46L10, 47A15

Milestones

Received: 11 September 1979

Published: 1 April 1981