## Rota’s theorem for general functional Hilbert spaces

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- by Joseph A. Ball
- Proc. Amer. Math. Soc.
**64**(1977), 55-61 - DOI: https://doi.org/10.1090/S0002-9939-1977-0461176-0
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## Abstract:

By a theorem of G.-C. Rota, every (linear) operator*T*on a Hilbert space with spectral radius less than one is similar to the adjoint of the unilateral shift

*S*of infinite multiplicity restricted to an invariant subspace. This theorem is shown to be true in a rather general context, where

*S*is multiplication by

*z*on a Hilbert space of functions analytic on an open subset

*D*of the complex plane, and

*T*is an operator with spectrum contained in

*D*. A several-variable version for an

*N*-tuple of commuting operators with a corollary concerning complete spectral sets is also presented.

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## Bibliographic Information

- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**64**(1977), 55-61 - MSC: Primary 47A45; Secondary 47A25
- DOI: https://doi.org/10.1090/S0002-9939-1977-0461176-0
- MathSciNet review: 0461176