## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Miniconference on Operators in Analysis. Ian Doust, Brian Jefferies, Chun Li, and Alan McIntosh, eds. Proceedings of the Centre for Mathematical Analysis, v. 24. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1990), 83 - 90

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416335062

**Mathematical Reviews number (MathSciNet)**

MR1060113

**Zentralblatt MATH identifier**

0718.47018

#### Citation

Doust, Ian. An example in the theory of spectral and well-bounded operators. Miniconference on Operators in Analysis, 83--90, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1990. https://projecteuclid.org/euclid.pcma/1416335062