The Completion of Generalized 2-Inner Product Spaces
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Abstract
A complete metric space is a well-known concept. Kreyszig shows that every non-complete metric space can be developed into a complete metric space , referred to as completion of .
We use the b-Cauchy sequence to form which “is the set of all b-Cauchy sequences equivalence classes”. After that, we prove to be a 2-normed space. Then, we construct an isometric by defining the function from to ; thus and are isometric, where is the subset of composed of the equivalence classes that contains constant b-Cauchy sequences. Finally, we prove that is dense in , is complete and the uniqueness of is up to isometrics
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References
Anshul, R.; Ravinder, K., S., ; Sumit, C., Stability of Complex Functional Equations in 2-Banach Spaces. Journal of Mathematical Physics, Analysis, Geometry . 2021, 17, 3, 341–368.
Bahram, D. ; Mohammad, J., Atomic Systems in 2-inner Product Spaces, Iranian Journal of Mathematical Sciences and Informatics. 2018, 13, 1, 103-110.
Cho, Y., J ;Freese, R. W., Geometry of Linear 2-Normed Spaces, Nova Science Publishers, New York, 2001.
Y. J. Cho, M. Matic, J. E., Pecaric, On Gram’s Deteminant in 2-Inner Product Spaces, J. Korean Math. Soc., 2001, 38(4), 1125–1156.
Debnath, P., Saha, M., Categorization of n-inner product space. Asian Res. J. Math. 2018,11(4), 1–10.
Ghafoor, G., R. ; Jamil, Z., Z., Study of b-Hilbert Spaces and Some Classes of Operators, University of Baghdad, Baghdad, 2018, 27-28.
Kreyszig, Erwin, Introductory Functional Analysis with Applications, John Wiley and Sons, New York, 1978.
Prasenjit, G., Frame operator for K-frame in 2-inner product space, International Journal of Mathematics Trends and Technology. 2021, 67.
Mazaheri, H.; Kazemi, R., Some Results on 2-Inner Product Spaces, Nove Sad. J.Math. 2007, 37, 35-40.
Riyas, P., ; Ravindran, K., T., Riesz Theorems and ~Adjoint Operators On Generalized 2-Inner Product Spaces, Global Journal mathematics, 2015, 3, 1, May 18, 244-254.
Sibel, E. Ideal Strong Lacunary Quasi Cauchy Sequences in 2-normed spaces. AIP Conference Proceedings 2334, 040004 .2021.
Vijayakumar, S.; Baskaran B., A Characterization of 2-Inner Product Spaces. AIP Conference Proceedings 2282, 020040 .2020.