Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-08T23:28:17.376Z Has data issue: false hasContentIssue false
  • English
  • Français

Automatic continuity of perturbations of casual operators

Published online by Cambridge University Press:  17 April 2009

K. J. Harrison ,
L-J. Eaton  and
J. A. Ward
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
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 281 - 291
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Johnson, B.E., ‘Continuity of homomorphisms of Banach G-modules’, Pacific J. Math. 120 (1985), 111–121.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), 403–414.CrossRefGoogle Scholar
[4]Sinclair, A.M., Automatic continuity of linear operators (Cambridge University Press, 1976).CrossRefGoogle Scholar