Canonical models for invariant subspaces

Michael John McAsey

Vol. 91 (1980), No. 2, 377–395

DOI: 10.2140/pjm.1980.91.377

Abstract

The invariant subspace structure of an operator algebra L₊ is completely determined. The non-selfadjoint algebra is constructed from a cyclic transformation acting on a finite set. There is a distinguished (finite) set of invariant subspaces of L₊ which has been identified elsewhere. These subspaces are used as canonical models; all other invariant subspaces for L₊ are described in terms of these subspaces. Uniqueness of this representation is also discussed.

Mathematical Subject Classification 2000

Primary: 47A15

Secondary: 47A45, 47D25

Milestones

Received: 20 April 1979

Published: 1 December 1980