Sub-exact Sequence on Hilbert Space
Bernadhita H. S. Utami *(a), Fitriani (b), Mustofa Usman (b), Warsono (b)

(a) Doctoral Program of Mathematics and Natural Science, Faculty of Mathematics and Natural Science, University of Lampung, Lampung, Indonesia
*bernadhita.herindri.s[at]mail.ugm.ac.id
(b) Department of Mathematics, Faculty of Mathematics and Natural Science, University of Lampung, Lampung, Indonesia

Abstract

The notion of the sub-exact sequence is the generalization of exact sequence in algebra especially on a module. A module over a ring R is a generalization of the notion of vector space over a field F. Refers to a special vector space over field F when we have a complete inner product space, it is called a Hilbert space. A space is complete if every Cauchy sequence converges. Now, we introduce the sub-exact sequence on Hilbert space which can later be useful in statistics. This paper aims to investigate the properties of the sub-exact sequence and their relation to direct summand on Hilbert space.

Keywords: complete inner product space, direct summand, Hilbert space, sub-exact sequence

Topic: Mathematics