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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Expanding the joint spectrum of pairs
of commuting contractions


Author: Adrian Ionescu
Journal: Proc. Amer. Math. Soc. 124 (1996), 3711-3719
MSC (1991): Primary 47A15; Secondary 30C20, 30D40, 47A13
MathSciNet review: 1340390
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Abstract: We present a connection between solving the invariant subspace problem for a single operator $T$ 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.


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Additional Information

Adrian Ionescu
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
Email: IONESCU_A@txlutheran.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03446-6
PII: S 0002-9939(96)03446-6
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