Open AccessSub-Exact Sequence On Hilbert Space
Author(s) -
Bernadhita Herindri Samodera Utami,
Fitriani Fitriani,
Mustofa Usman,
Warsono,
Jamal Ibrahim Daoud
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1751/1/012022
Subject(s) - exact sequence , hilbert space , sequence (biology) , mathematics , generalization , isomorphism (crystallography) , quotient space (topology) , field (mathematics) , space (punctuation) , vector space , sequence space , hilbert series and hilbert polynomial , inner product space , pure mathematics , mathematical analysis , banach space , computer science , quotient , crystal structure , genetics , chemistry , biology , crystallography , operating system
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. As the result, we get two properties of isometric isomorphism sub-exact sequence on Hilbert space.