Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T01:06:27.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear operators whose domain is locally convex

Published online by Cambridge University Press:  20 January 2009

N. J. Kalton
N. J. Kalton
Affiliation:
University College of Swansea, Singleton Park, Swansea. SA2 8PP
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.

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on S separates the points of S. If X is a Banach space and T : X → F is a continuous linear operator, then T is quasi-convex if is quasi-convex, where U is the unit ball of X.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 4 , September 1977 , pp. 293 - 299
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCES

(1) Alexiewicz, A. and Semadeni, Z., Linear functionals on two-norm spaces, Studia Math. 17 (1958), 121–140.CrossRefGoogle Scholar
(2) Bartle, R. G., Dunford, N. and Schwartz, J. T., Weakcompactness and vector measures, Canad. J. Math. 7 (1955), 289–305.CrossRefGoogle Scholar
(3) Bessaga, C. and Pelczyński, A., The estimated extension theorem, homogeneous collections and skeletons, and their applications to the topological classification of linear metric spaces and convex sets, Fund. Math. 59 (1970), 113–190.Google Scholar
(4) Brooks, J. K., On the existence of a control measure for strongly bounded vector measures, Bull. Amer. Math. Soc. 77 (1971), 999–1001.CrossRefGoogle Scholar
(5) Christensen, J. P. R. and Herer, W., On the existence of pathological submeasures and the construction of exotic topological groups, Math. Ann. 213 (1975), 203–210.Google Scholar
(6) Dazord, J. and Jourlin, M., Une topologie mixte sur l'espace L∞, Publ. Dept. Math. Lyons 11, 2 (1974), 1–18.Google Scholar
(7) Drewnowski, L., On control submeasures and measures, Studia Math. 50 (1974), 203–224.CrossRefGoogle Scholar
(8) Hoffman-Jorgensen, J., Vector measures, Math. Scand. 28 (1971), 5–32.CrossRefGoogle Scholar
(9) Jamison, R. E., O'Brien, R. C. and Taylor, P. D., On embedding a compact convex set into a locally convex topological vector space, Pacific J. Math. (to appear).Google Scholar
(10) Kalton, N. J., Basic sequences in F-spaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151–167.CrossRefGoogle Scholar
(11) Kalton, N. J., Exhaustive operators and vector measures, Proc. Edinburgh Math. Soc. 19 (1975), 291–300.CrossRefGoogle Scholar
(12) Labuda, I., Sur la theoreme de Bartle-Dunford-Schwartz, Bull. Acad. Polon. Sci. 20 (1972), 557–561.Google Scholar
(13) Maharam, D., An algebraic characterization of measure algebras, Ann. of Math. 48 (1947), 154–167.CrossRefGoogle Scholar
(14) Musial, K., Absolute continuity of vector measures, Coll. Math. 27 (1973), 319–321.CrossRefGoogle Scholar
(15) Musial, K., Absolute continuity and the range of group-valued measures, Bull. Acad. Polon. Sci. 21 (1972), 105–113.Google Scholar
(16) Peck, N. T. and Waelbroeck, L., Problem 58, Proceedings of the International Colloquium on Nuclear Spaces and Ideals in Operator Algebras, Warsaw,18-25 June 1969, Studia Math 48 (1970), 482.Google Scholar
(17) Phelps, R. R., Dentability and extreme points in Banach spaces, J. Functional Analysis 17 (1974), 78–90.CrossRefGoogle Scholar
(18) Stegall, C., The Radon-Nikodym property in conjugate Banach spaces, Trans. Amer. Math. Soc. 206 (1975), 213–223.CrossRefGoogle Scholar
(19) Stroyan, K. D., A characterization of the Mackey uniformity on (L∞, L1) for finite measures, Pacific J. Math. 49 (1973), 223–228.CrossRefGoogle Scholar
(20) Turpin, P., Convexites dans les espaces vectorials topologiques generaux (These, Orsay, 1974).Google Scholar
(21) Wiweger, A., Linear spaces with mixed topology, Studia Math. 20 (1961), 47–68.CrossRefGoogle Scholar