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Mat. Zametki, 2015, Volume 98, Issue 1, Pages 61–75 (Mi mz10500)  

Goursat's Lemma in the Context of Banach Algebras

E. A. Gorin


Abstract: The classical Goursat lemma is extended to classes of differentiable mappings of domains of real Banach spaces to algebras of linear operators acting on these spaces. We clarify the modification of the form and content of this lemma in dependence on the choice of the original object. The case in which the original space is a Banach algebra and Fréchet derivatives are operators of multiplication by elements of this algebra is considered separately.

Keywords: Goursat lemma, Banach space, Banach algebra, Fréchet derivative.

DOI: https://doi.org/10.4213/mzm10500

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English version:
Mathematical Notes, 2015, 98:1, 78–89

Bibliographic databases:

UDC: 517.986
Received: 26.02.2014

Citation: E. A. Gorin, “Goursat's Lemma in the Context of Banach Algebras”, Mat. Zametki, 98:1 (2015), 61–75; Math. Notes, 98:1 (2015), 78–89

Citation in format AMSBIB
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