Study of Finite Dimensional Topological Vector Spaces

Authors

  • Rakesh Kumar Bharti  Research Scholar, Department of Mathematics, J. P. University, Chapra. Bihar, India
  • Surendra Ray  Research Scholar, Department of Mathematics, B. R. A. Bihar University, Muzaffarpur, Bihar, India.
  • Dr. Rajnarayan Singh  Department of Mathematics, Jagdam College, Chapra, J. P. University, Chapra, Bihar, India.

Keywords:

TVS, Finite Dimensional Spaces, Linear Topology Spaces, Hausdorff Space.

Abstract

In this present paper, we studied about finite dimensional topological vector spaces. In general analysis it is customary to study linear spaces for which there is defined a "norm," which takes the place of the absolute value of ordinary analysis in defining distance, limit point, continuity, and so on. Linear metric spaces more general than the normed spaces have also been studied by Fréchet, Banach, and several others.

References

  1. Q. Bu, J. Diestel: Observations about the projective tensor product of Banach space p ⊗X, 1 < p <∞. Quaestiones Mathematicae 24 (2001), 519-533.
  2. W. Congxin, Q. Bu: K¨othe dual of Banach spaces pE] (1 ≤ p < ∞) and Grothendieck space. Comment. Math. Univ. Carolinae 34, (2) (1993), 265-273.
  3. N. De Grande-De Kimpe: Generalized Sequence spaces. Bull. Soc. Math. Belgique, 23 (1971), 123-166.
  4. M. Gupta, Q. Bu: On Banach-valued sequence spaces pX]. J. Anal. 2 (1994), 103-113.
  5. D. W. Dean: The equation L(E, X∗∗)= L(E, X)∗∗ and the principle of the local reflexivity. Proc. Amer. Math. Soc., 40 (1973), 146-148.
  6. H. Jarchow: Locally convex spaces. B. G. Teubner Stuttgart (1981).
  7. G. K¨othe: Topological Vector Spaces I and II. Springer-Verlag, Berlin, Heidelberg, New York.

International Journal of Scientific Research in Science and Technology

Downloads

Published

2022-04-30

Issue

Volume 9, Issue 2, March-April-2022

Section

Research Articles

License

Copyright (c) IJSRST

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Rakesh Kumar Bharti, Surendra Ray, Dr. Rajnarayan Singh "Study of Finite Dimensional Topological Vector Spaces" International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011,Volume 9, Issue 2, pp.425-427, March-April-2022.