A Note on Hilbert Modules
Introduction and preliminaries Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the natural generalization that of Hilbert spaces arising by replacing of the field of scalars C by a C∗-algebra. Let us recall some basic facts about the Hilbert C∗-modules....
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| Format: | Article |
| Language: | fas |
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Kharazmi University
2021-09-01
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| Series: | پژوهشهای ریاضی |
| Subjects: | |
| Online Access: | http://mmr.khu.ac.ir/article-1-2806-en.html |
| _version_ | 1797871672666095616 |
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| author | Abbas Sahleh Leila Najarpisheh |
| author_facet | Abbas Sahleh Leila Najarpisheh |
| author_sort | Abbas Sahleh |
| collection | DOAJ |
| description | Introduction and preliminaries
Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the natural generalization that of Hilbert spaces arising by replacing of the field of scalars C by a C∗-algebra. Let us recall some basic facts about the Hilbert C∗-modules.
Let A be a C∗-algebra. An right inner product A-module is a linear space X which is a right A-module (with compatible scalar multiplication: λ(x.a) =(λx).a = x.(λa) for x ∈ X, a ∈ A, λ ∈ C), together with a map (x, y)→ : X × X → A such that for all x, y, z ∈ X, a ∈ A, α, β ∈ C./files/site1/files/72/10Abstract.pdf |
| first_indexed | 2024-04-10T00:47:34Z |
| format | Article |
| id | doaj.art-b6d19a381498458f9a4105fbdbf5f89b |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:47:34Z |
| publishDate | 2021-09-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | پژوهشهای ریاضی |
| spelling | doaj.art-b6d19a381498458f9a4105fbdbf5f89b2023-03-13T19:22:49ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542021-09-0172311316A Note on Hilbert ModulesAbbas Sahleh0Leila Najarpisheh1 Introduction and preliminaries Hilbert C∗-modules were firrst introduced in the work of I. Kaplansky.Hilbert C*-modules are the natural generalization that of Hilbert spaces arising by replacing of the field of scalars C by a C∗-algebra. Let us recall some basic facts about the Hilbert C∗-modules. Let A be a C∗-algebra. An right inner product A-module is a linear space X which is a right A-module (with compatible scalar multiplication: λ(x.a) =(λx).a = x.(λa) for x ∈ X, a ∈ A, λ ∈ C), together with a map (x, y)→ : X × X → A such that for all x, y, z ∈ X, a ∈ A, α, β ∈ C./files/site1/files/72/10Abstract.pdfhttp://mmr.khu.ac.ir/article-1-2806-en.htmlc*- hilbert modulebanach algebrac* algebrad-derivation |
| spellingShingle | Abbas Sahleh Leila Najarpisheh A Note on Hilbert Modules پژوهشهای ریاضی c*- hilbert module banach algebra c* algebra d-derivation |
| title | A Note on Hilbert Modules |
| title_full | A Note on Hilbert Modules |
| title_fullStr | A Note on Hilbert Modules |
| title_full_unstemmed | A Note on Hilbert Modules |
| title_short | A Note on Hilbert Modules |
| title_sort | note on hilbert modules |
| topic | c*- hilbert module banach algebra c* algebra d-derivation |
| url | http://mmr.khu.ac.ir/article-1-2806-en.html |
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