help, I don't know how to try the following
- if T is an isometry then $TT^\star$it's a projection
- if T, S are two normal operators $ST=TS$ and S is compact , then $S+T$ and $ST$ They are normal.
Any help would be most appreciated.
2026-04-08 11:22:32.1775647352
help with normal linear operators and projections
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$P=T^*T$ is an orthogonal projection iff $P^2=P=P^*$. To show this, using $T^*T=I$, $$ (TT^*)^2=T(T^*T)T^*=TT^* \\ (TT^*)^*= TT^* $$