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ESTIMATES FOR FRACTIONAL POWERS AND LOGARITHM OF OPERATORS WITH HILBERT-SCHMIDT RESOLVENTS AND PERTURBATION RESULTS
Let A be a closed operator on a separable Hilbert space with the spectrum in the open right half-plane and a bounded Hermitian component, and let the resolvent of A be a Hilbert-Schmidt operator.The paper deals with the functionwhere µ is a nondecreasing function and I is the unit operator.We …