Finding The HK Completions of Some Sequence Spaces

Husain

doi:https://doi.org/10.54216/PMTCS.030203

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Volume 3 • Issue 2 • PP: 40-43 • 2024

Finding The HK Completions of Some Sequence Spaces

Husain Alhayek ^1*

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¹Hama University, Department of Mathematics, Hama, Syria

* Corresponding Author.

DOI https://doi.org/10.54216/PMTCS.030203

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Received: June 21, 2023 Revised: September 14, 2023 Accepted: December 15, 2023

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Abstract

In this paper, we prove the following result: If the space (the finite sequences) is equipped with the norm which is naturally induced by a positive definite Hermitian and diagonally blockwise constructed matrix, then an HK completion exists. Also, we investigate our result through many illustrated examples.

Keywords

HK completion vector space normed space sequence

References

[1] A. Wilansky, "Sununability Through Functional Analysis", North Holand - N.Y. 1984.

[2] 2.book, "Modern Methods in Topological Vactor Spaces" 1978.

[3] 3.book, "Topics in Functional Analysis", Springer-verlag, N.Y. 1967.

[4] 4. book, "Functional Analysis", 1964.

[5] 5. A. Mukherjed and K. Pothoven, "Real and Functional Analysis", 1978,

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Alhayek, Husain. "Finding The HK Completions of Some Sequence Spaces." Pure Mathematics for Theoretical Computer Science, vol. Volume 3, no. Issue 2, 2024, pp. 40-43. DOI: https://doi.org/10.54216/PMTCS.030203

Alhayek, H. (2024). Finding The HK Completions of Some Sequence Spaces. Pure Mathematics for Theoretical Computer Science, Volume 3(Issue 2), 40-43. DOI: https://doi.org/10.54216/PMTCS.030203

Alhayek, Husain. "Finding The HK Completions of Some Sequence Spaces." Pure Mathematics for Theoretical Computer Science Volume 3, no. Issue 2 (2024): 40-43. DOI: https://doi.org/10.54216/PMTCS.030203

Alhayek, H. (2024) 'Finding The HK Completions of Some Sequence Spaces', Pure Mathematics for Theoretical Computer Science, Volume 3(Issue 2), pp. 40-43. DOI: https://doi.org/10.54216/PMTCS.030203

Alhayek H. Finding The HK Completions of Some Sequence Spaces. Pure Mathematics for Theoretical Computer Science. 2024;Volume 3(Issue 2):40-43. DOI: https://doi.org/10.54216/PMTCS.030203

H. Alhayek, "Finding The HK Completions of Some Sequence Spaces," Pure Mathematics for Theoretical Computer Science, vol. Volume 3, no. Issue 2, pp. 40-43, 2024. DOI: https://doi.org/10.54216/PMTCS.030203

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