Open AccessA generalization of Lomonosov’s inequality and its applications to invariant subspaces
Author(s) -
Shamim I. Ansari
Publication year - 2002
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-02-06644-3
Subject(s) - linear subspace , invariant (physics) , mathematics , compact space , property (philosophy) , generalization , pure mathematics , class (philosophy) , inequality , reflexive operator algebra , algebra over a field , discrete mathematics , mathematical analysis , computer science , mathematical physics , philosophy , compact operator , epistemology , extension (predicate logic) , artificial intelligence , programming language
In this article we generalize Victor Lomonosov’s famous inequality so as to be applicable to a wider class of functions. Then using it we prove that the adjoint of an algebra with a compactness property which is weaker than the PS property, employed by Victor Lomonosov, has nontrivial invariant subspaces.