Expanding the joint spectrum of pairs of commuting contractions
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- by Adrian Ionescu PDF
- Proc. Amer. Math. Soc. 124 (1996), 3711-3719 Request permission
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.References
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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
- Received by editor(s): August 24, 1994
- Received by editor(s) in revised form: May 9, 1995
- Communicated by: Theodore W. Gamelin
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3711-3719
- MSC (1991): Primary 47A15; Secondary 30C20, 30D40, 47A13
- DOI: https://doi.org/10.1090/S0002-9939-96-03446-6
- MathSciNet review: 1340390