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Expanding the Joint Spectrum of Pairs of Commuting Contractions

Adrian Ionescu
Proceedings of the American Mathematical Society
Vol. 124, No. 12 (Dec., 1996), pp. 3711-3719
Stable URL: http://www.jstor.org/stable/2161541
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Expanding the Joint Spectrum of Pairs of Commuting Contractions
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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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