پژوهشهای ریاضی (Sep 2021)
A Note on Hilbert Modules
Abstract
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
