Compressions of Resolvents and Maximal Radius of Regularity
نویسنده
چکیده
Suppose that λ − T is left-invertible in L(H) for all λ ∈ Ω, where Ω is an open subset of the complex plane. Then an operator-valued function L(λ) is a left resolvent of T in Ω if and only if T has an extension T̃ , the resolvent of which is a dilation of L(λ) of a particular form. Generalized resolvents exist on every open set U , with U included in the regular domain of T . This implies a formula for the maximal radius of regularity of T in terms of the spectral radius of its generalized inverses. A solution to an open problem raised by J. Zemánek is obtained.
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