Higher weak derivatives and reflexive algebras of operators

Abstract

Let D be a self-adjoint operator on a Hilbert space H and x a bounded operator on H. We say that x is n times weakly D−differentiable, if for any pair of vectors ξ, η from H the function 〈eitDxe−itDξ, η〉 is n times differentiable. We give several characterizations of n times weak dif-ferentiability, among which, one is original. These results are used to show that for a von Neumann algebra M on H the algebra of n times weakly D−differentiable operators in M has a natural representation as a reflexive subalgebra of B(H ⊗ ℂ(n+1)).

Original languageEnglish
Title of host publicationOperator Algebras and Their Applications : A Tribute to Richard V. Kadison
EditorsRobert S. Doran, Efton Park
PublisherAmerican Mathematical Society
Publication date2016
Pages69-83
ISBN (Print)978-1-4704-1948-6
ISBN (Electronic)978-1-4704-3500-4
Publication statusPublished - 2016
SeriesContemporary Mathematics
Volume671
ISSN0271-4132

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