Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-10-28T04:33:53.029Z Has data issue: false hasContentIssue false

Automatic continuity of perturbations of casual operators

Published online by Cambridge University Press:  17 April 2009

K. J. Harrison
Affiliation:
Division of Science, Murdoch University, Murdoch WA 6150, Australia e-mail: [email protected]@[email protected]
L-J. Eaton
Affiliation:
Division of Science, Murdoch University, Murdoch WA 6150, Australia e-mail: [email protected]@[email protected]
J. A. Ward
Affiliation:
Division of Science, Murdoch University, Murdoch WA 6150, Australia e-mail: [email protected]@[email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain automatic continuity results for finite-rank perturbations of causal sequence space operators, and provide examples to illustrate cases where automatic continuity does not hold.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Johnson, B.E., ‘Continuity of homomorphisms of Banach G-modules’, Pacific J. Math. 120 (1985), 111121.CrossRefGoogle Scholar
[2]Ramsey, L.T., ‘Bounded-in-bounded-out, linear, causal operators on causal sequences have finite gain’, (preprint).Google Scholar
[3]Saeki, S., ‘Discontinuous translation invariant functionals’, Trans. Amer. Math. Soc. 282 (1984), 403414.CrossRefGoogle Scholar
[4]Sinclair, A.M., Automatic continuity of linear operators (Cambridge University Press, 1976).CrossRefGoogle Scholar