An example in the theory of spectral and well-bounded operators
Ian Doust · Project Euclid (Cornell University) · 1990
An example is given of a linear transformation which defines a wellbounded operator on $L^p[O, 1] for 1 \\leq p \\leq \\infty$. It is shown that the properties of the decomposition of the identity associated with this operator (and consequently the type of functional calculus that the operator admits) vary markedly depending on the domain space.