Measure, Integration & Real Analysis · Problem 10B.4

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · spectrum-bounded-operators

Problem

Suppose

E

is a nonempty closed bounded subset of

\mathbf{F}

. Show that there exists

T \in \mathcal{B}(\ell^2)

such that

\mathrm{sp}(T) = E