Invariant subspaces and limits of similarities
by
Srdjan Petrovic
Western Michigan University
Coauthors: Alan Lambert (University of North Carolina Charlotte)

Let {D_j: j=1, 2, ...} be a sequence of bounded invertible operators on Hilbert space H and denote by M = {T: lim_{n --> \infty} D_nTD_n^-1 exists }. Then M is a (not necessarily closed) subalgebra of L(H), and the mapping \phi: M --> \LH defined as \phi(T) = lim_{n --> \infty} D_nTD_n^-1 is an algebra homomorphism. We show that under certain conditions on the sequence {D_j: j=1, 2, ...}, the algebra M has a nontrivial invariant subspace. Specific examples this sequence are considered leading to some invariant subspace theorems.

Date received: April 30, 1999