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Galoitica: Journal of Mathematical Structures and Applications

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Online: 2834-5568
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Continuous publication

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Open access journal. All articles are freely available online with no APC.

Galoitica: Journal of Mathematical Structures and Applications
Full Length Article

Volume 5Issue 2PP: 08-11 • 2023

A Study on Compact Operators in Locally K -Convex Spaces

Karla Zayood 1*
1Online Islamic University, Department Of Science and Information Technology, Doha, Qatar
* Corresponding Author.
Received: December 11, 2022 Revised: April 13, 2023 Accepted: May 02, 2023

Abstract

In this paper we give an equivalent definition of continuous and compact linear operators by using orthogonal bases in non-archimedean locally K - convex spaces. We also show that if E is a  space and F is a semi-Montel  space, then every continuous linear operator T:EF is compact.

Keywords

Operator Convex space Compact set

References

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[3] C. C. Perez-Garcia and W.H. Schikhof, Compact operators and the Orlicz-Pettis property in p-adic analysis, Report 9101, Department of Math, Catholic University, Nijmegen, the Netherlands, 1991, 1 27.

[4] C. Perez-Garcia, On compactoidity in non-Archimedean locally convex spaces with a Schauder basis, Nederl. Akad. Wetensch. Indag., 50,(1988), 85-88.

[5] W.H. Schikhof, Locally convex spaces over non-spherically complete valued fields, I-II, Bull. Soc. Math. Belgique, XXXVIII (ser. B),38, (1986), 187-224.

[6] A. C. M. Van Rooij, Non-Archimedean Functional Analysis, Marcel Dekker, New York, (1978).

[7] V.P. Zahariuta, On the isomorphism of Cartesian products of locally convex spaces, Studia Math. 46, (1973), 201-221.

[8] Multu, F., Tercan, A., and Yasar, R., Eventually semisimple weak FI-extending modules, Mathematica BOHEMICA, Vol 148, 2023

[9] Yasar, R., C11-modules via left exact modules preradicals, Turkish journal of mathematics, vol 45, 2021.

[10] Yasar, R., On weak Projection invariant semisimple modules, Fundamental journal of mathematics and applications, 2021.

[11] Yasar, R., and Tercan, A., Extending property on EC-fully submodules, Sakarya university Journal of Science, 2018.

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Zayood, Karla. "A Study on Compact Operators in Locally K -Convex Spaces." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 5, no. Issue 2, 2023, pp. 08-11. DOI: https://doi.org/10.54216/GJMSA.050201
Zayood, K. (2023). A Study on Compact Operators in Locally K -Convex Spaces. Galoitica: Journal of Mathematical Structures and Applications, Volume 5(Issue 2), 08-11. DOI: https://doi.org/10.54216/GJMSA.050201
Zayood, Karla. "A Study on Compact Operators in Locally K -Convex Spaces." Galoitica: Journal of Mathematical Structures and Applications Volume 5, no. Issue 2 (2023): 08-11. DOI: https://doi.org/10.54216/GJMSA.050201
Zayood, K. (2023) 'A Study on Compact Operators in Locally K -Convex Spaces', Galoitica: Journal of Mathematical Structures and Applications, Volume 5(Issue 2), pp. 08-11. DOI: https://doi.org/10.54216/GJMSA.050201
Zayood K. A Study on Compact Operators in Locally K -Convex Spaces. Galoitica: Journal of Mathematical Structures and Applications. 2023;Volume 5(Issue 2):08-11. DOI: https://doi.org/10.54216/GJMSA.050201
K. Zayood, "A Study on Compact Operators in Locally K -Convex Spaces," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 5, no. Issue 2, pp. 08-11, 2023. DOI: https://doi.org/10.54216/GJMSA.050201
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