Every linear transformation can be decomposed in sum of unitary operators

Question

Let $V$ an unitary space and $T: V \rightarrow V$ a linear transformation. Find $U_1$ and $U_2$ unitary transformations such that $T= U_1 + iU_2$.

I think is related with this analogous question in matrices but I am clueless how to reduce it in two operators.

How could I prove it?

This can't be true. Take $v\mapsto 3v$. – Amitai Yuval May 06 '17 at 16:38 — Amitai Yuval, May 06 '17 at 16:38

score 0 · Answer 1 · answered May 06 '17 at 19:26

0

Let T, K and L be linear transformations such that K = 1/2(T'+T) and L = (1/2)(1/i)(T'-T) where T' is the adjoint of T. and see that T = K+iL

answered May 06 '17 at 19:26

grets feal

1 Answers1