@inbook{ba75c97d121c4fbdbe161a7116113524,
title = "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)).",
author = "Erik Christensen",
year = "2016",
language = "English",
isbn = "978-1-4704-1948-6",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "69--83",
editor = "Doran, {Robert S.} and Park, {Efton }",
booktitle = "Operator Algebras and Their Applications",
address = "United States",
}