can someone please help me to answer the following problem:
Let (ek) be a total orthonormal sequence in a separable Hilbert space H and
Let T: H→H be defined at ek by: T(ek) = ek+1. , k = 1, 2··· and then linearly
and continuously extended to H.
a) Find invariant subspaces.
b)show that T has no eigenvalues
Let (ek) be a total orthonormal sequence in a separable Hilbert space H and
Let T: H→H be defined at ek by: T(ek) = ek+1. , k = 1, 2··· and then linearly
and continuously extended to H.
a) Find invariant subspaces.
b)show that T has no eigenvalues