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UPA Perpustakaan Universitas Jember

A characterization of Hilbert C∗-modules over commutative C∗-algebras

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Let M be a Hilbert C∗-module. Set |x| =
x, x
1
2 for every x ∈ M and C
= {

x, y

: x, y ∈ M}. We prove that |xa|=|x||a| for every x ∈ M and a ∈ C if and only
if C is a commutative C∗-algebra.
Ke

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