Galoitica: Journal of Mathematical Structures and Applications

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https://doi.org/10.54216/GJSMA

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Galoitica: Journal of Mathematical Structures and Applications

Volume 5 , Issue 2 , PP: 08-11, 2023 | Cite this article as | XML | Html | PDF

A Study on Compact Operators in Locally K -Convex Spaces

Karla Zayood 1 *

  • 1 Online Islamic University, Department Of Science and Information Technology, Doha, Qatar - (zayyyoood134@gmail.com)
  • Doi: https://doi.org/10.54216/GJMSA.050201

    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

    [1] N.De Grande-De Kimpe, On the structure of locally K-convex spaces with a Schauder basis, Indag. Math., 34 (1972), 396-406.

    [2] N.De Grande-De Kimpe, C-compactness in locally K-convex spaces, Indag. Math., 33, (1971), 176-180.

    [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.

    Cite This Article As :
    Karla Zayood. "A Study on Compact Operators in Locally K -Convex Spaces." Full Length Article, Vol. 5, No. 2, 2023 ,PP. 08-11 (Doi   :  https://doi.org/10.54216/GJMSA.050201)
    Karla Zayood. (2023). A Study on Compact Operators in Locally K -Convex Spaces. Journal of , 5 ( 2 ), 08-11 (Doi   :  https://doi.org/10.54216/GJMSA.050201)
    Karla Zayood. "A Study on Compact Operators in Locally K -Convex Spaces." Journal of , 5 no. 2 (2023): 08-11 (Doi   :  https://doi.org/10.54216/GJMSA.050201)
    Karla Zayood. (2023). A Study on Compact Operators in Locally K -Convex Spaces. Journal of , 5 ( 2 ), 08-11 (Doi   :  https://doi.org/10.54216/GJMSA.050201)
    Karla Zayood. A Study on Compact Operators in Locally K -Convex Spaces. Journal of , (2023); 5 ( 2 ): 08-11 (Doi   :  https://doi.org/10.54216/GJMSA.050201)
    Karla Zayood, A Study on Compact Operators in Locally K -Convex Spaces, Journal of , Vol. 5 , No. 2 , (2023) : 08-11 (Doi   :  https://doi.org/10.54216/GJMSA.050201)