Sub-Exact Sequence on Hilbert Space | Zendy

Bernadhita Herindri Samodera Utami | Zendy; Fitriani Fitriani | Zendy; Mustofa Usman | Zendy; Warsono | Zendy; Jamal Ibrahim Daoud | Zendy

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Sub-Exact Sequence on Hilbert Space

Author(s) -

Bernadhita Herindri Samodera Utami,

Fitriani Fitriani,

Mustofa Usman,

Warsono,

Jamal Ibrahim Daoud

Publication year - 2020

Publication title -

journal of southwest jiaotong university

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.

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