×

Some characterizations of p-adic semi-Fredholm operators. (English) Zbl 0728.47045

A semi-Fredholm operator T: \(E\to F\), between two Banach spaces over some complete non-archimedean valued field K, is a continuous linear map such that dim(ker T)\(<\infty\) and im T is closed in F. In Banach spaces there are notions of t-orthogonal subset and compactoid subsets. The paper translates the condition “semi-Fredholm” in terms of preservation of t- orthogonality and compactoid subset.

MSC:

47S10 Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory
47A53 (Semi-) Fredholm operators; index theories
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gruson, L., Théorie de Fredholm p-adigue, Bull. Soc. Math. France, 94, 67-95 (1966) · Zbl 0149.34702
[2] Martinez-Maurica, J.; Pellon, Teresa, Preservation of closed sets under non-archimedean operators, Proc. Kon. Ned. Akad. v. Wet. A, 90, 63-68 (1987) · Zbl 0624.46053
[3] Van Rooij, A. C. M., Non-archimedean Functional Analysis (1979), New York: Marcel Dekker, New York · Zbl 0938.46513
[4] Van Rooij, A. C. M., Notes on p-adic Banach Spaces, Report (1976), Nijmegen: Katholieke Universiteit, Nijmegen
[5] Serre, J. P., Endomorphisms complètement continus des espaces de Banach p-adiques, Inst. Hautes Etudes Sci. Publ. Math., 12, 69-85 (1962) · Zbl 0104.33601
[6] Shilkret, W., Orthogonal transformations in non-archimedean spaces, Arch. Math., XXIII, 285-291 (1972) · Zbl 0238.47026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.