Some operators on finite-dimensional non-Archimedean normed spaces

Authors

  • M. Babahmed Department of Mathematics, University of Moulay Ismail, Faculty of Sciences, Meknes, Morocco.

DOI:

https://doi.org/10.17398/

Keywords:

Non-Archimedean normed space, t-Orthogonal basis, p-delta function, Simple operator, Similarity, Isometry, Expansion

Abstract

In this paper, we are interested in the study of certain operators in non-Archimedean normed spaces of finite dimension. We introduce the notion of p-delta function, then we characterize the simple operators, the similarities and the expansions. We show if E has an orthogonal basis, then each injective operator on E is the composition of an isometry and an expansion.

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References

J. Cabello Sánchez, J. Navarro Garmendia, Isometries of ultrametric normed spaces, Ann. Funct. Anal. 12 (2021), 11 pp., DOI: 10.1007/s43034-021-00144-7.

A. Kubzdela, Isometries, Mazur–Ulam theorem and Aleksandrov problem for non-Archimedean normed spaces, Nonlinear Analysis: Theory, Methods and Applications, 75, pp. 2060-2068 (2012) DOI: 10.1016/j.na.2011.10.006.

A.F. Monna, Analyse Non-archimédienne, Berlin-Springer (1970).

C. Perez-Garcı́a, W.H. Schikkof, Locally Convex Spaces over non-Archimedean valued fields, Cambridge Studies in Advanced Mathematics 119, (2010).

A.C.M. van Rooij, Non-Archimedean Functional analysis, New York, Dekker, (1978).

A.C.M. van Rooij, Notes on p-Adic Banach Spaces, Report 7633, Math. Inst. Kathol. Univ. Nijmegen, (1976).

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Published

2024-08-05

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How to Cite

Some operators on finite-dimensional non-Archimedean normed spaces. (2024). Extracta Mathematicae. https://doi.org/10.17398/