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• W3100707267 abstract "It is proved that the resolvent norm of an operator with a compact resolvent on a Banach space cannot be constant on an open set if the underlying space or its dual is complex strictly convex. It is also shown that this is not the case for an arbitrary Banach space: there exists a separable, reflexive space and an unbounded, densely defined operator acting in with a compact resolvent whose norm is constant in a neighbourhood of zero; moreover is isometric to a Hilbert space on a subspace of co-dimension 2. There is also a bounded linear operator acting on the same space whose resolvent norm is constant in a neighbourhood of zero. It is shown that similar examples cannot exist in the co-dimension 1 case." @default.
• W3100707267 created "2020-11-23" @default.
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• W3100707267 date "2015-06-26" @default.
• W3100707267 modified "2023-09-26" @default.
• W3100707267 title "LEVEL SETS OF THE RESOLVENT NORM OF A LINEAR OPERATOR REVISITED" @default.
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• W3100707267 doi "https://doi.org/10.1112/s0025579315000194" @default.
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