Hostname: page-component-7479d7b7d-767nl Total loading time: 0 Render date: 2024-07-13T12:27:00.281Z Has data issue: false hasContentIssue false
  • English
  • Français

On the surjectivity of linear maps on locally convex spaces

Published online by Cambridge University Press:  09 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra A.C.T., Australia
Rights & Permissions [Opens in a new window]

Abstract

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.

The aim of this note is to investigate the structure of general surjectivity problem for a continuous linear map between locally convex spaces. We shall do so by using the method introduced in Yamamuro (1980). Its basic notion is that of calibrations which has been introduced in Yamamuro (1975), studied in detail in Yamamuro (1979) and appliced to several problems in Yamamuro (1978) and Yamamuro (1979a).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 2 , April 1982 , pp. 187 - 211
Copyright
Copyright © Australian Mathematical Society 1982

References

Colombeau, J. F. (1979), ‘Infinite dimensional C∞-mappings with a given sequence of derivatives at a given point’, J. Math. Anal. Appl. 71, 95–104.CrossRefGoogle Scholar
Dieudonné, J. (1969), Foundations of modern analysis, (Academic Press, New York and London).Google Scholar
Köthe, G. (1967), Topological vector spaces I, (Springer-Verlag, Berlin, Heiderberg, New York).Google Scholar
Köthe, G. (1979), Topological vector spaces II, (Springer-Verlag, Berlin, Heiderberg, New York).CrossRefGoogle Scholar
Malgrange, B. (1966), Ideals of differentiable functions, (Studies in Mathematics 3, Oxford University Press, London).Google Scholar
Mennicken, R. and Sagraloff, B. (1980), ‘Characterization of nearly openness’, J. Reine Angew. Math. 313, 105–115.Google Scholar
Treves, F. (1967), Locally convex spaces and linear partial differential equations, (Springer-Verlag, Berlin, Heiderberg, New York).CrossRefGoogle Scholar
Yamamuro, S. (1974), Differential calculus in topological linear spaces, (Lecture Notes in Mathematics 374, Springer-Verlag, Berlin, Heiderberg, New York).CrossRefGoogle Scholar
Yamamuro, S. (1975), ‘A differentiation in locally convex spaces’, Bull. Austral. Math. Soc. 12, 183–209.CrossRefGoogle Scholar
Yamamuro, S. (1978), ‘A note on Omori-Lie groups’, Bull. Austral. Math. Soc. 19, 333–349.CrossRefGoogle Scholar
Yarnamuro, S. (1979), A theory of differentiation in locally convex spaces, (Mem. Amer. Math. Soc. 1, no. 212, Providence, R.I.).Google Scholar
Yamamuro, S. (1979a), ‘A note on the Omega lemma’, Bull. Austral. Math. Soc. 20, 421–435.CrossRefGoogle Scholar
Yamamuro, S. (1980), ‘Notes on the inverse mapping theorem in locally convex spaces’, Bull. Austral. Math. Soc. 21, 419–461.CrossRefGoogle Scholar