Proceedings of the Centre for Mathematics and its Applications

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

Ian Doust

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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

Source
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

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


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