On the Mazur-Ulam theorem on Fréchet algebras

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-06-0098

Keywords:

Mazur-Ulam theorem, Fréchet algebras, Isometry, Affine map

Abstract

The Mazur-Ulam Theorem on Frechet Algebras is proved.

Author Biographies

Abbas Zivari-Kazempour, Ayatollah Borujerdi University.

Dept. of Mathematics.

M. R. Omidi, Kermanshah University of Technology.

Dept. of Basic Sciences.

References

S. Banach, Theorie des opérations lineaires. Warsaw, 1932.

T. Figiel, P. Šemrl, and J. Väisälä, “Isometries of normed spaces”, Colloquium mathematics, vol. 92, no. 1, pp. 153-154, 2002, doi: 10.4064/cm92-1-13

M. Fragoulopoulou, Topological algebras with involution. Burlington: North-Holland, 2005.

A. Mallios, Topological algebras, Burlington: North-Holland, 1986.

S. Mazur and S. Ulam, Sur les transformations isométriques d’espaces vectoriels normés, Comptes Rendus de l'Académie des Sciences Paris, vol. 194, pp. 946-948, 1932.

E. A. Michael, Locally multiplicatively convex topological algebras, Providence, RI: American Mathematics Society, 1952.

B. Nica, “The Mazur-Ulam theorem”, Expositiones mathematicae, vol. 30, no. 4, pp. 397-398, 2012, doi: 10.1016/j.exmath.2012.08.010

J. Väisälä, “A proof of the Mazur-Ulam theorem”, The American mathematical monthly, vol. 110, no. 7, pp. 633-635, 2003, doi: 10.2307/3647749

Published

2020-11-12

How to Cite

[1]
A. Zivari-Kazempour and M. R. Omidi, “On the Mazur-Ulam theorem on Fréchet algebras”, Proyecciones (Antofagasta, On line), vol. 39, no. 6, Nov. 2020.

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