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Matematicheskie Zametki, 1971, Volume 10, Issue 2, Pages 207–218 (Mi mzm9705)  
Formula for the differentiation of operator-valued functions depending on a parameter

V. I. Burenkov

Moscow Institute of Radio Engineering, Electronics, and Automation
Full-text PDF (1266 kB)
Abstract: A study of the convergence of the differentiation formula
$$ (f(A))'=f'(A)A'+\frac{f''(A)}{2!}[A'A]+\frac{f'''(A)}{3!}[[A'A]A]+\dots, $$
where $[XY]=XY-YX$, and $A=A(t)$ is a function of the real variable $t$ with values in a Banach algebra.
Received: 06.06.1970
English version:
Mathematical Notes, 1971, Volume 10, Issue 2, Pages 546–552
DOI: https://doi.org/10.1007/BF01822880
Bibliographic databases:
Document Type: Article
UDC: 517.4
Language: Russian
Citation: V. I. Burenkov, “Formula for the differentiation of operator-valued functions depending on a parameter”, Mat. Zametki, 10:2 (1971), 207–218; Math. Notes, 10:2 (1971), 546–552
Citation in format AMSBIB
\Bibitem{Bur71}
\by V.~I.~Burenkov
\paper Formula for the differentiation of operator-valued functions depending on a parameter
\jour Mat. Zametki
\yr 1971
\vol 10
\issue 2
\pages 207--218
\mathnet{http://mi.mathnet.ru/mzm9705}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=512220}
\zmath{https://zbmath.org/?q=an:0216.41201}
\transl
\jour Math. Notes
\yr 1971
\vol 10
\issue 2
\pages 546--552
\crossref{https://doi.org/10.1007/BF01822880}
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