Complutense University Library

Spaces of weakly continuous functions.

Ferrera Cuesta, Juan (1982) Spaces of weakly continuous functions. Pacific Journal of Mathematics , 102 (2). pp. 285-291. ISSN 0030-8730

[img] PDF
Restricted to Repository staff only until 31 December 2020.

756kB

Official URL: http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.pjm/1102724443&page=record

View download statistics for this eprint

==>>> Export to other formats

Abstract

This paper is very much in the spirit of a paper by H. Corson [Trans. Amer. Math. Soc. 101 (1961),
1–15; MR0132375 (24 2220)]. Let E be a real Banach space. The bw-topology on E is the finest
topology which agrees with the weak topology on all bounded subsets of E. Cwb(E) [Cwbu(E)]
is the set of real functions which are weakly continuous [weakly uniformly continuous] on all
bounded sets in E. Cwb(E) is always barrelled; a sufficient condition is given for Cwb(E) to be
bornological (under the compact-open topology). As a main result, the following are shown to be
equivalent: (1) E is reflexive; (ii) Cwbu(E) is a Fr´echet space; (iii) Cwbu(E) is a Pt´ak space; (iv)
Cwbu(E) is complete; (v) Cwbu(E) is barrelled; (vi) Cwbu(E) = Cwb(E).


Item Type:Article
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:15380
References:

H. H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc , 101 (1961), 1-15.

J. Diestel, Geometry of Banach Spaces, Selected Topics. Lect. Notes in Math., 485 Springer-Verlag, New York, 1975.

J. Ferrera J. Gomez and J. L. G. Llavona, On completion of spaces of weakly continuous, functions, to appear in J. London Math. Soc.

L. Gilman and M. Jerison, Rings of Continuous Functions, Van Norstrand, 1960.

J. Kelley, General Topology, Springer.

G. Kothe, Topological Vector Spaces I, Springer-Verlag, New York, 1969.

L. Nachbin, Topological vector spaces of continuous functions, Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 471-474.

T. Shirota, On locally convex vector spaces of continuous functions, Proc. Japan Acad., 30 (1954), 294-298.

M. Talagrand, Sur une conjecture de B. H. Corson, Bull. Sci. Math., (2), 99 (1975), 211-212.

M. Valdivίa, Some new results on weak compactness, J. Functional Anal., 24 (1977), 1-10.

S. Warner, The topology of compact convergence on continuous function spaces, Duke Math. J., 25, 265-282.

Deposited On:28 May 2012 08:33
Last Modified:06 Feb 2014 10:23

Repository Staff Only: item control page