Differentiation of operator functions and perturbation bounds

Bhatia, Rajendra ; Singh, Dinesh ; Sinha, Kalyan B. (1998) Differentiation of operator functions and perturbation bounds Communications in Mathematical Physics, 191 (3). pp. 603-611. ISSN 0010-3616

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Official URL: http://www.springerlink.com/index/M6RR4LMETGRT7YNH...

Related URL: http://dx.doi.org/10.1007/s002200050279


Given a smooth real function f on the positive half line consider the induced map on the set of positive Hilbert space operators. Let f (k<) /E5> be the k th derivative of the real function f and > E5 > D k f the k th Frechet derivative of the operator map f. We identify large classes of functions for which , for k= 1,2,... . This reduction of a noncommutative problem to a commutative one makes it easy to obtain perturbation bounds for several operator maps. Our techniques serve to illustrate the use of a formalism for "quantum analysis" that is like the one recently developed by M. Suzuki.

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