Expanding the joint spectrum of pairs
of commuting contractions
Abstract: We present a connection between solving the invariant subspace problem for a single operator on Hilbert space and the existence of a common invariant subspace for two commuting related operators. In particular, we reduce the problem of the existence of nontrivial invariant subspaces for a single contraction with spectral radius one to the problem of the existence of common nontrivial invariant subspaces for a pair of commuting contractions with large joint spectra.
Affiliation: Department of Mathematics and Computer Science, Texas Lutheran University, Seguin, Texas 78155; Institute of Mathematics of the Romanian Academy, PO Box 1-764, RO-70700 Bucharest, Romania
Received by editor(s): August 24, 1994
Received by editor(s) in revised form: May 9, 1995
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1996 American Mathematical Society