Volume 7, Issue 2 (Vol.7, No. 2, 2021)
mmr 2021, 7(2): 311-316 |
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Sahleh A, Najarpisheh L. A Note on Hilbert Modules. mmr 2021; 7 (2) :311-316
URL: http://mmr.khu.ac.ir/article-1-2806-en.html
URL: http://mmr.khu.ac.ir/article-1-2806-en.html
1- , sahlehj@guilan.ac.ir
Abstract: (1617 Views)
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
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
Type of Study: Original Manuscript |
Subject:
alg
Received: 2018/07/4 | Revised: 2021/08/8 | Accepted: 2020/02/3 | Published: 2021/09/1 | ePublished: 2021/09/1
Received: 2018/07/4 | Revised: 2021/08/8 | Accepted: 2020/02/3 | Published: 2021/09/1 | ePublished: 2021/09/1
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