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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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 |
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