I have a question on (orthogonal) direct sums of an Operator.
In particular, I was wondering if the direct summands of a linear and bounded operator $T$ on a complex Hilbertspace $H$ are all $T$-reducible closed subspaces, where a subspace $M$ is reducible if $T(M)\subset M$ and $T(M^\perp)\subset M^\perp$. Is that true, and if so, why?
I don't know much about direct sums of operators, and the statement I proposed is what I was able to derive from here: Formal definition of direct sum of operators.
thanks in advance