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Quasinilpotent Operators and the Invariant Subspace Problem
Author(s) -
Read C. J.
Publication year - 1997
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/s0024610797005486
Subject(s) - linear subspace , invariant subspace , invariant (physics) , invariant subspace problem , subspace topology , mathematics , construct (python library) , simple (philosophy) , pure mathematics , banach space , algebra over a field , discrete mathematics , computer science , approximation property , epistemology , mathematical analysis , unbounded operator , philosophy , mathematical physics , programming language
In this paper we construct quasinilpotent operators without nontrivial invariant subspaces. As well as being interesting in its own right, we believe that this is a sensible (perhaps necessary) first step for addressing the difficult problem of constructing topologically simple Banach algebras.