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Proceedings of the American Mathematical Society

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Differentiability of the exponential of a member of a near-ring


Author: J. W. Neuberger
Journal: Proc. Amer. Math. Soc. 48 (1975), 98-100
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1975-0370194-0
MathSciNet review: 0370194
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Abstract: Suppose $ S$ is a Banach space and $ K$ is the near-ring of all zero preserving Lipschitz transformations from $ S$ to $ S$. It is shown that all exponentials of members of $ K$ have certain differentiability properties. This leads to the fact that no neighborhood of the identity transformation is filled with exponentials of members of $ K$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0370194-0
Keywords: Identity component, normed near-ring exponential
Article copyright: © Copyright 1975 American Mathematical Society

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