Sub-exact sequence on Hilbert space
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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English English |
| Published: |
IOP Publishing Ltd
2021
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/93696/8/93696_Sub-exact%20sequence.pdf http://irep.iium.edu.my/93696/9/93696_Sub-exact%20sequence%20on%20hilbert%20space_Scopus.pdf http://irep.iium.edu.my/93696/ https://iopscience.iop.org/article/10.1088/1742-6596/1751/1/012022/meta |
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| Institution: | Universiti Islam Antarabangsa Malaysia |
| Language: | English English |
| Summary: | 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 |
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