# Hilber space and linear bounded operator

Let H be a Hilbert space and A: H-> H be a Linear Bounded Operator. Show that A can be written as A=B+C where B and C are Linear Bounded Operators and B is self-adjoint and C is skew.

This is suppose to be an easy question but i'm not sure where to start.
I know that self-adjoint is (B*=B) and skew is (C*=-C) but can someone show this?

## Answers and Replies

morphism
Homework Helper
Hint: A+A* is self-adjoint. Can you find a similar expression that's skew? Then what?

A-A* is skew
so A = B+B* + C-C*?

morphism
Homework Helper
What are B and C?

HallsofIvy