Expanding the joint spectrum of pairs of commuting contractions

Ionescu, Adrian

doi:10.1090/S0002-9939-96-03446-6

Expanding the joint spectrum of pairs of commuting contractions
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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.

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