i try to understand a few isomorphisms, which i have found without comment in a text:
Let H be a Hilbert space and Then we have the following identities:
I know that we can decompose the Space H by
And by the isomorphism above (1) we get
Analogue we have also a decomposition
But then the text says:
Are these equations always true? I mean T is bounded in this case, but isn't it necessary that T is injective or something like that? It would be nice, if someone can explain those eqations to me.