## Proceedings of the Centre for Mathematics and its Applications

### An example in the theory of spectral and well-bounded operators

Ian Doust

#### Abstract

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.

#### Article information

Dates
First available in Project Euclid: 18 November 2014