Abstract
AbstractLet H and T: H → H denote a separable Hilbert space and an operator in a Schatten‐von Neumann ideal Sp(H), respectively. Consider the resolvent operator (λI ‐ T)−1, where I is the identity operator and λ belongs to the resolvent set of T. Some sharp bounds for the uniform operator norm of (λI ‐ T)−1 are derived in some situations of particular interest for certain applications, namely when only partial or minimal information about the spectrum is available. The results obtained may also be regarded as generalizations of Carleman's inequality for quasinilpotent operators.
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