If the $A^A\leq BB^$ and $B$ is a compact operator, then the operator $A$ is compact

66 Views Asked by Bumbble Comm At 26 Mar 2026 - 7:33

I am a student of mathematics and professor left us today for homework this example:

If the $A^*A\leq BB^*$ and $B$ is a compact operator, then the operator $A$ is compact. Prove this. ($A^*$ hermitian adjoint operator)

Thanks very much for your help. Previously thank you for your solution.