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A Non‐Separable Reflexive Banach Space on Which there are Few Operators
Author(s) -
Wark H. M.
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002393
Subject(s) - mathematics , approximation property , separable space , finite rank operator , pseudo monotone operator , bounded operator , banach space , bounded function , compact operator , operator (biology) , reflexive space , pure mathematics , strictly singular operator , c0 semigroup , operator space , discrete mathematics , mathematical analysis , interpolation space , computer science , functional analysis , biochemistry , chemistry , repressor , transcription factor , extension (predicate logic) , gene , programming language
It is shown that there exists a non‐separable reflexive Banach space on which every bounded linear operator is the sum of a scalar multiple of the identity operator and an operator of separable range. There is a strong sense that such a Banach space has as few operators as its linear and topological properties allow.