Finding The HK Completions of Some Sequence Spaces

Husain Alhayek

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

Pure Mathematics for Theoretical Computer Science

Finding The HK Completions of Some Sequence Spaces

Husain Alhayek ^{1
*}

1 Hama University, Department of Mathematics, Hama, Syria - (Hayekalhusain333@gmail.com)

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

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

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,

Cite This Article As :

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

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