Open AccessSub-Exact Sequence on Hilbert Space
Author(s) -
Bernadhita Herindri Samodera Utami,
Fitriani Fitriani,
Mustofa Usman,
Warsono,
Jamal Ibrahim Daoud
Publication year - 2020
Publication title -
xi'nan jiaotong daxue xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 21
ISSN - 0258-2724
DOI - 10.35741/issn.0258-2724.55.6.34
Subject(s) - exact sequence , hilbert space , sequence (biology) , mathematics , quotient space (topology) , isomorphism (crystallography) , generalization , hilbert series and hilbert polynomial , space (punctuation) , field (mathematics) , sequence space , rigged hilbert space , vector space , reproducing kernel hilbert space , hilbert manifold , pure mathematics , mathematical analysis , banach space , computer science , quotient , crystal structure , chemistry , biology , crystallography , operating system , genetics
The notion of the sub-exact sequence is the generalization of exact sequence in algebra, particularly on a module. A module over a ring R is a generalization of the notion of vector space over a field F. A Hilbert space refers to a special vector space over a field F when we have a complete inner product space. The space is complete if every Cauchy sequence converges. Now, we introduce the sub-exact sequence on a Hilbert space, which can be useful later in statistics. This paper is aimed at investigating the properties of the sub-exact sequence and their ratio to direct summand on a Hilbert space. As the result, we obtain two properties of isometric isomorphism sub-exact sequence on a Hilbert space.