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

Full text not available from this repository.

Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00243...

Related URL: http://dx.doi.org/10.1016/S0024-3795(99)00084-1

Abstract

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

Repository Staff Only: item control page