International Journal of Statistics and Applied Mathematics
  • Printed Journal
  • Indexed Journal
  • Refereed Journal
  • Peer Reviewed Journal

2023, Vol. 8, Issue 4, Part A

A note on spaces of operators on Hilbert spaces


Author(s): Dr. Amar Nath Kumar

Abstract:
In this research paper, we explained and established the results for the space of operators in Hilbert space. Some of them are if the space of all operators on a Hilbert space H, B(H) is a Banach Space as well as here we construct a set of operators R on a Hilbert space H in the following way R = {Ti: Ti2 = 0, TiTj = 0} and we have proved that R is a Banach Space. Also If R and R’ be linear spaces and T: R → R’ be a linear transformation then Kernel T is a linear subspace of R. We discussed on isomorphism concept also here if T be a linear transformation of R onto R’ then T is an isomorphism if and only if Ker T = {0}. We have also discussed algebraic structure, we have seen that the set of all non-singular transformations on a linear space R forms a group with respect to multiplication.


Pages: 21-25 | Views: 220 | Downloads: 22

Download Full Article: Click Here

International Journal of Statistics and Applied Mathematics
How to cite this article:
Dr. Amar Nath Kumar. A note on spaces of operators on Hilbert spaces . Int J Stat Appl Math 2023;8(4):21-25.

Call for book chapter
International Journal of Statistics and Applied Mathematics