I have seen the following estimation in some proofs: $A^*B^*BA \leq ||B||_{op}^2 \,A^*A$ for $A,B\in B(H)$
I don't see where this inequality comes from. Do you have a proof? Thanks for your help.
2026-04-01 22:01:55.1775080915
Estimation for operators
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$$\|B\|^2A^*A-A^*B^*BA=A^*(\|B\|^2I-B^*B)A\ge 0$$