Mosco convergence in locally convex spaces

S. L. Zabell*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let E and F be a pair of locally convex spaces in duality, with σ and τ the weak and Mackey topologies on E. A sequence of functions {fn} on E is said to be Mosco-convergent to another function f0, denoted fn M → f0, if for every v ε{lunate} E, lim supn → t8 fn(vn) ≤ f0(v) for some sequence vn t → v, and lim infn → ∞ fn(vn) ≥ f0(v) for every sequence vn δ → v. In this paper it is shown that if F is a separable Fréchet space, {fn: n ≥ 1} a sequence of proper, lower semicontinuous convex functions, and fn* the convex conjugate of fn, then fn M → f0 ⇒ f*n M → f*n if f0(v) < ∞ for some v ε{lunate} E.

Original languageEnglish (US)
Pages (from-to)226-246
Number of pages21
JournalJournal of Functional Analysis
Volume110
Issue number1
DOIs
StatePublished - Nov 15 1992

ASJC Scopus subject areas

  • Analysis

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