Abstract
Representations of some algebras of functions in the commutant of an almost isometric operator (i.e., a trace class perturbation of an isometry) are constructed. The properties of these representations are investigated. In particular, an analog of the class C0 for contractions is discovered: it is shown that an operator is singular (i.e., the boundary values of its resolvent from inside and outside the disk coincide) if an only if there exists a nonzero function ϕ for which ϕ(T)=0. Bibliography: 7 titles.
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 59–73.
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Kapustin, V.V. Function calculus for almost isometric operators. J Math Sci 85, 1794–1801 (1997). https://doi.org/10.1007/BF02355289
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DOI: https://doi.org/10.1007/BF02355289