A-BEST APPROXIMATION IN PRE-HILBERT C∗-MODULES
Abstract
While there have been many number of studies about
best approximation in some spaces, there has been little work
on pre-Hilbert C-modules. Here we provide such a study that
lead to a number of approximation theorems. In particular, some
results about existence and uniqueness of best approximation of
submodules on Hilbert C-modules are also presented. This will
done by considering the C-algebra valued map x → |x| where
|x| = ⟨x; x⟩ 1
2 . Also we show that when K is a convex subset of
a pre- Hilbert C-module X; it is a Chebyshev set with respect
to C- valued norm which is dened on X. In the end, we study
various properties of an A-valued metric projection onto a convex
set or a submodule.
best approximation in some spaces, there has been little work
on pre-Hilbert C-modules. Here we provide such a study that
lead to a number of approximation theorems. In particular, some
results about existence and uniqueness of best approximation of
submodules on Hilbert C-modules are also presented. This will
done by considering the C-algebra valued map x → |x| where
|x| = ⟨x; x⟩ 1
2 . Also we show that when K is a convex subset of
a pre- Hilbert C-module X; it is a Chebyshev set with respect
to C- valued norm which is dened on X. In the end, we study
various properties of an A-valued metric projection onto a convex
set or a submodule.
Keywords
Best approximation, C * -algebras, pre- C * -module.
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