International Journal of Modern Science and Technology · ISSN 2456-0235

Research Article · Mathematical Sciences · Volume 3, Issue 6 · Jun 2018 · Pages 126–132

Certain Properties of Hilbert Space Operators

N. B. Okelo

  • N. B. Okelo: School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya.

Abstract

Let H be an infinite dimensional Hilbert space and B(H) the algebra of all bounded linear operators in H. In this paper, we characterize certain properties of operators on Hilbert spaces. These include: norm and singular value inequalities. We have proved that if A has closed range and the Moore-Penrose inverse A⁺ and if we let X vary in NA(H), where A A* AX=A*. Then A⁺ belongs to NA(H) and si(X)≥si (A⁺) for i  1, 2,... .We have given extensions to other classes for example the norm-attainable class.

Keywords

Hilbert space; Norm; Inequalities; Norm-attainability

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