Invariant subspaces of a direct sum of weighted shifts

Eric Albert Nordgren

Vol. 27 (1968), No. 3, 587–598

DOI: 10.2140/pjm.1968.27.587

Abstract

The invariant subspaces of a direct sum of finitely many copies of the adjoint of a monotone 1² shift are shown to be spanned by the finite dimensional invariant subspaces that they include. For the case of two copies of such a shift, the invariant subspaces are characterized in terms of a spanning set of vectors, and all infinite dimensional invariant subspaces are shown to be cyclic.

Mathematical Subject Classification

Primary: 47.35

Milestones

Received: 28 August 1967

Published: 1 December 1968