Study of a Compact Operator

Authors

  • Prof. Mushtaque Khan Professor of Mathematics, K. R. College, Gopalganj, J. P. University, Chapra, India Author
  • Nasim Akhtar Research Scholar, University Department of Mathematics, J. P. University, Chapra, India Author

Keywords:

Topology, Compact Operators, Vector- Space, Hilbert Spaces, Homomorphic, Functional Analysis

Abstract

In this present paper, we studied a compact operator. The purpose of this paper is to first review some concepts from Functional Analysis and Operator Algebra, then to apply these concepts to an in-depth introduction to Compact Operators and the Spectra of Compact Operators, leading to The Fredholm Alternative. [1-13].

Downloads

Download data is not yet available.

References

Bryon Rynne and M.A. Youngson, Linear Functional Analysis (2nd Edition), Springer-Verlag London Limited (2008).

B´ela Bollob´as, Linear Analysis (2nd Edition), Cambridge University Press (1999).

Richard Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems (4th Edition), Pearson Education Inc. (2004).

David J. Griffiths, Introduction to Quantum Mechanics (2nd Edition), Pearson Education Inc. (2005).

H. Apiola: Duality between spaces of p-summing operators and characterization of nuclearity. Math. Ann. 219, (1974), 53-64.

Q. Bu, J. Diestel: Observations about the projective tensor product of Banach space p ⊗X, 1 < p <∞. Quaestiones Mathematicae 24 (2001), 519-533.

W. Congxin, Q. Bu: K¨othe dual of Banach spaces p[E] (1 ≤ p < ∞) and Grothendieck space. Comment. Math. Univ. Carolinae 34, (2) (1993), 265-273.

N. De Grande-De Kimpe: Generalized Sequence spaces. Bull. Soc. Math. Belgique, 23 (1971), 123-166.

M. Gupta, Q. Bu: On Banach-valued sequence spaces p[X]. J. Anal. 2 (1994), 103-113.

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.

H. Jarchow: Locally convex spaces. B. G. Teubner Stuttgart (1981).

G. K¨othe: Topological Vector Spaces I and II. Springer-Verlag, Berlin, Heidelberg, New York.

M. A. Ould Sidaty: Reflexivity and AK-property of certain vector sequence spaces. Bull. Belg. Math. Soc., Simon Stevin 10 (4) (2003), 579-783.

Downloads

Published

15-05-2024

Issue

Section

Research Articles

How to Cite

Study of a Compact Operator . (2024). International Journal of Scientific Research in Science and Technology, 11(3), 837-839. https://ijsrst.com/index.php/home/article/view/IJSRST24113249

Similar Articles

1-10 of 120

You may also start an advanced similarity search for this article.