Variation of real powers of positive operators

Bhatia, Rajendra ; Sinha, Kalyan B. (1994) Variation of real powers of positive operators Indiana University Mathematics Journal, 43 (3). pp. 913-925. ISSN 0022-2518

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For each real number p consider the map f(A)=Ap on the set of positive operators in a Hilbert space. Let Df(A) denote the Fréchet derivative of this map at A. In an earlier paper it was shown that ||Df(A)||=||pAp−1|| when 0≤p≤1. Here we show that this is true also when p &<0 and when p≥2 but not when 1&<p&<√2. Some other functions are also discussed.

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Deposited On:11 Feb 2013 05:06
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