I have the following problem:
Let H be a Hilbert space
a) Prove that if $T: H\to H$ is compact then $T^2$ is compact operator
b) Find $S: H\to H$ compact such that $S=T^2$ with T non compact
c)If T is self adjoint then $T^2$ compact implies T is compact.
I have managed to prove (a). Can anyone give me any idea for the other requests. Thank you in advance.