Paul O Oleche, Naftali O Ongati, John O Agure (JOOUST, 2009)
A bounded operator with the spectrum lying in a compact set V ⊂
R, has C∞(V ) functional calculus. On the other hand, an operator H acting on
a Hilbert space H, admits a C(R) functional calculus if H is self-adjoint. So ...