Polar Decomposition: Approximation

80 Views Asked by At

Given a C*-algebra $\mathcal{A}$.

Polar Decomposition: $$\forall A\in\mathcal{A}\exists V_\varepsilon\in\mathcal{A}:\quad A=V_\varepsilon|A|^{1-\varepsilon}\quad(\varepsilon>0)$$

How can I construct this?

Similar statement: Wegge-Olsen, Exercise 1.A.c