Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-28T10:10:57.413Z Has data issue: false hasContentIssue false
  • English
  • Français

Some special operators and new classes of locally convex spaces

Published online by Cambridge University Press:  24 October 2008

Ajit Kaur Chilana
Ajit Kaur Chilana
Affiliation:
Newnham College, Cambridge and Hindu College, Delhi
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider some special operators on a locally convex Hausdorff space to itself, which have neat spectral theories and prove some perturbation results. This leads us to define and study a few special classes of locally convex spaces in which various subsets of the algebra of continuous linear operators either coincide or are closely related with each other. These are then compared to the classes of barrelled, infrabarrelled and DF-spaces and examples are given to distinguish them from one another.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 3 , May 1972 , pp. 475 - 489
Copyright
Copyright © Cambridge Philosophical Society 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Allan, G. R.A spectral theory for locally convex algebras. Proc. London Math. Soc. (3) 15 (1965), 399–421.Google Scholar
(2)Chilana, A. K.Relatively continuous linear operators and some perturbation results. J. London Math. Soc. (2) 2 (1970), 225–231.Google Scholar
(3)Chilana, A. K.Invariant subspaces for linear operators in locally convex spaces. J. London Math. Soc. (2) 2 (1970), 493–503.CrossRefGoogle Scholar
(4)Chilana, A. K.Contributions to the theory of linear operators in locally convex spaces. Ph.D. Dissertation, Cambridge University, 1969.Google Scholar
(5)Gohberg, I. C. and Krein, M. G.The basic propositions on defect numbers, root numbers and indices of linear operators. Uspehi Mat. Nauk. (N.S.) 12 (1957) No. 2 (74), 43–118.(Russian). Amer. Math. Soc. Trans. (2), 13 (1960), 185–264.Google Scholar
(6)Grothendieck, A.Sur les espaces (F) et (DF). Summa Brasil. Math. 3 (1954), 57–123.Google Scholar
(7)Kato, T.Perturbation theory for linear operators (Springer Verlag, Berlin, Heidelberg, New York, 1966).Google Scholar
(8)Kato, T.Perturbation theory for nullity, deficiency and other quantities of linear operators. J. Analyse Math. 6 (1958), 261–322.CrossRefGoogle Scholar
(9)Köthe, G.Topological vector spaces I (Springer Verlag New York Inc. 1969). (English Translation of Topologische Lineare Raume I, 1966 (First edition 1960), by D. J. H. Garling, 1969).Google Scholar
(10)Michael, E. A.Locally multiplicatively-convex topological algebras. Mem. Amer. Math. Soc. 11 (1952).Google Scholar
(11)Moore, R. T.Banach algebras of operators on locally convex spaces. Bull. Amer. Math. Soc. 75 (1969), 68–73.Google Scholar
(12)Schaefer, H. H.Topological vector spaces. (Macmillan, 1964).Google Scholar
(13)Webb, J. H.Sequential convergence in locally convex spaces. Proc. Cambridge Philos. Soc. 64 (1968), 341–364.Google Scholar
(14)Wiweger, A.Linear spaces with mixed topology. Studia Math. 20 (1961), 47–68.Google Scholar
(15)Chilana, A. K. Some perturbation results for linear operators in locally convex spaces. To appear in the Proc. London Math. Soc.Google Scholar