Growth conditions and similarity orbits

Ghatage, P.

doi:10.1090/S0002-9939-1977-0448132-3

Growth conditions and similarity orbits
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Proc. Amer. Math. Soc. 65 (1977), 127-130 Request permission

Abstract:

It is proved that an operator T which acts on a separable Hilbert space and whose resolvent satisfies a first-order growth condition inside and outside the unit circle, can be approximated in norm by operators which are similar to a single unitary operator. In particular the ’Markus-operator’ can be approximated by similarities of a diagonal unitary operator and is a compact perturbation of the same.

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