On the Existence of Invariant Subspaces and Reflexivity of N-Tuples of Operators

Abstract

Recent results concerning the existence of a common nontrivial invariant subspace and reflexivity for families of commuting linear bounded Hilbert space operators will be presented; starting with the families of linear transformations on finite dimensional space, through families of isometries, jointly quasinormal operators and spherical isometries, finishing with N -tuples of contractions with dominating spectra. This paper is based On the notes for the series of lectures given in the De-

Joint local quasinilpotence and common invariant subspaces

“…The concept of joint quasinilpotence plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8].…”

“…Positive results about N-tuples of operators with a nontrivial common invariant subspace have been obtained in [2,4,7,8]. In this article, we extend the results of Abramovich et al [1] to the case of not-necessarily commuting N-tuples of continuous linear operators.…”