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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
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$.

References [Enhancements On Off] (What's this?)

  • [1] M. Nagumo, Einige analytische Untersuchunger in linearen metrischen Ringen, Japan J. Math. 13 (1936), 61-80.
  • [2] J. W. Neuberger, Toward a characterization of the identity component of rings and near-rings of continuous transformations, J. Reine Angew. Math. 238 (1969), 100–104. MR 0250144
  • [3] J. v. Neumann, Über die analytischen Eigenschaften von Gruppen linearer Transformationen und ihrer Darstellungen, Math. Z. 30 (1929), no. 1, 3–42 (German). MR 1545040, 10.1007/BF01187749

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Keywords: Identity component, normed near-ring exponential
Article copyright: © Copyright 1975 American Mathematical Society