Rotaβs theorem for general functional Hilbert spaces
Author:
Joseph A. Ball
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Reproducing kernel function,
Riesz-Dunford functional calculus,
similarity,
complete spectral set and normal dilation
Article copyright:
© Copyright 1977
American Mathematical Society
