The Semi-Algebra Generated by a Compact Linear Operator
- 1 June 1965
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 14 (3), 177-196
- https://doi.org/10.1017/s0013091500008774
Abstract
We prove that if t is a compact linear operator that is not quasi-nilpotent and is appropriately normalised, then the closed semi-algebra A(t) generated by t is locally compact. The theory of locally compact semi-algebras (2) is therefore applicable to A(t), and we show that it can be used to obtain spectral properties of t.Keywords
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