Derivations, derivatives and chain rules

Bhatia, Rajendra ; Sinha, Kalyan B. (1999) Derivations, derivatives and chain rules Linear Algebra and its Applications, 302-303 . pp. 231-244. ISSN 0024-3795

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For a smooth function f on the space of bounded operators in a Hilbert space, we obtain formulas for the nth order commutator [[[f(A),X],X],...,X] in terms of the Frechet derivatives Dmf(A). We illustrate the use of these formulas in obtaining bounds for norms of generalised commutators f(A)X-Xf(B) and their higher order analogues.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Fréchet Derivative; Derivation; Commutator; Perturbation Bound
ID Code:2592
Deposited On:08 Oct 2010 07:11
Last Modified:17 May 2011 04:57

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