Differentiability of the exponential of a member of a near-ring
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- by J. W. Neuberger PDF
- Proc. Amer. Math. Soc. 48 (1975), 98-100 Request permission
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
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M. Nagumo, Einige analytische Untersuchunger in linearen metrischen Ringen, Japan J. Math. 13 (1936), 61-80.
- 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 250144, DOI 10.1515/crll.1969.238.100
- 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, DOI 10.1007/BF01187749
Additional Information
- © Copyright 1975 American Mathematical Society
- 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