The canonical form of a scalar operator on a Banach space

G. D. Faulkner, J. E. Huneycutt
1978 Proceedings of the American Mathematical Society  
Let A = f XdE(X) be a scalar operator on a Banach space X. If there exists a vector g S X such that the closed convex hull of the range of the vector measure /i(-) = E(-)g has nonvoid interior, then A is similar to the operator Qf (A) = \f(\) on a quotient space of a suitably constructed £°°s pace.
doi:10.1090/s0002-9939-1978-0487577-3 fatcat:qcdtq5dt7bae7bhdyyn2xn6mei