Dear MHF members,
I have a functional analysis problem as follows.
Problem. Let denote the map on the unit circle of the complex plane .
For , let be the mapping for .
- Show that the map is a unital -homomorphism of to .
Conclude that is a unitary.
- Show that , while .
- Show that is a proper dense subspace of .
is the set of continuous functions.
is the set of bounded operators.
is the set of square integrable functions.
and stand for the spectrum and the point spectrum, respectively.
-homomorphism - Star-Homomorphism -- from Wolfram MathWorld
-algebra - C*-Algebra -- from Wolfram MathWorld