Let H and K be Hilbert spaces.
Let $T: H \to K$ be a bounded operator. Is it true that $\|T\|^3= \|TT^{\ast}T\|$
I think it should be true but I can’t see the proof of this. Any hints or ideas?
2026-03-30 05:29:11.1774848551
Norm of an operator of $B(H,K)$
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$$ \|TT^*T\|^2 = \|(TT^*T)(TT^*T)^*\| = \|(TT^*)^3\| = \|TT^*\|^3 = \|T\|^6, $$ where the second-to last inequality can be proven by the spectral theorem for self-adjoint operators.