Can you help me with this. I don’t know what to do
Let R, S, T are linear operators, where V is a complex inner product space.
(i) Suppose that S is an isometry and R is a positive operator such that T=SR. Prove that R=square root of (T*T)
(ii) Let σ denote the smallest singular value of T, and let σ*denote the largest singular value of T. Prove that σ<=|| T(v)/||v|| ||<= σ* for every nonzero v in V.
Thanks