Measure, Integration & Real Analysis · Problem 10B.3

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · spectrum-eigenvalues

Problem

Suppose

E

is a bounded subset of

\mathbf{F}

. Show that there exists a Hilbert space

V

and

T \in \mathcal{B}(V)

such that the set of eigenvalues of

T

equals

E