On analyticity of local resolvents and existence of spectral subspaces

Fong, Che Kao

doi:10.1090/S0002-9939-1977-0445307-4

On analyticity of local resolvents and existence of spectral subspaces
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Proc. Amer. Math. Soc. 65 (1977), 99-102 Request permission

Abstract:

We present some sufficient conditions for a function from an open set in C into a Hilbert space H such that $(T - z)f(z) = x(T \in B(H)$ and $x \in H$) to be analytic. As an application we show that hyperinvariant subspaces exist for certain class of operators.

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