Premium
On the level sets of the resolvent norm of a linear operator
Author(s) -
Shargorodsky E.
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn038
Subject(s) - resolvent formalism , mathematics , resolvent , bounded operator , finite rank operator , bounded function , hilbert space , operator norm , compact operator , norm (philosophy) , operator space , banach space , pure mathematics , c0 semigroup , weak operator topology , operator (biology) , linear map , multiplication operator , linear operators , quasinormal operator , mathematical analysis , extension (predicate logic) , biochemistry , chemistry , repressor , law , political science , transcription factor , gene , computer science , programming language
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.