My teacher gave me a problem:
I have two self-adjoint operators $A$ and $B$. Both of them are greater or equal than $I$, i.e. $A \geq I$ and $B \geq I$. I need to to prove that there is a positive bounded operator $T$ for which $B=TAT$.
But I don't understand what means greater or equal for operators and i don't have any idea how to solve this problem. Would be glad for any help.
2026-03-25 17:34:06.1774460046
Self-adjoint operator as composition of bounded and self-adjoint
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