Let S = I + T^{\ast}T : H \longrightarrow H, where T is linear and bounded.
Show that S^{-1} S(H) \longrightarrow H exists.
(I is the Identity operator)
Let S = I + T^{\ast}T : H \longrightarrow H, where T is linear and bounded.
Show that S^{-1} S(H) \longrightarrow H exists.
(I is the Identity operator)
Hint.
I'm lost as to how to use this to find a solution for the question.
Letetc
and consider
You 'll also need to guarantee this converges.