Eugene Shargorodsky
Abstract
We construct a bounded linear operator on a Banach space and a closed densely defined operator on a Hilbert space with resolvent norms that are constant in a neighbourhood of zero. We also discuss cases where the norm of the resolvent of a bounded linear operator cannot be constant on an open set.
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We construct a bounded linear operator on a Banach space and a closed densely defined operator on a Hilbert space with resolvent norms that are constant in a neighbourhood of zero. We also discuss cases where the norm of the resolvent of a bounded linear operator cannot be constant on an open set.
Key concepts: Resolvent formalism, Mathematics, Resolvent, Bounded operator, Finite-rank operator, Bounded function, Hilbert space, Operator norm