1
vote
1answer
85 views

Approximation of certain continuous functions by analytic functions

Let $f\in C(S^{1},M_{n}(\mathbb{C}))$ be a unitary. Does there exist an analytic unitary function $g$ from $S^{1}$ to $M_{n}(\mathbb{C})$ that approximates $f$?
3
votes
2answers
141 views

How does this imply surjectivity? An application of the Tietze extension theorem.

Consider the functor $C$ from the category of compact Hausdorff spaces to that of unital abelian C*-algebras given by $C: X \mapsto C(X, \mathbb{C})$ (the continuous maps from $X$ to $\mathbb{C}$) and ...