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Invariants in abstract mapping pairs

Part of: Topological linear spaces and related structures Nonlinear operators and their properties

Published online by Cambridge University Press:  09 April 2009

Li Ronglu  and
Wang Junming
Li Ronglu
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Wang Junming
Affiliation:
Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China e-mail: [email protected]
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Abstract

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In a topological vector space, duality invariant is a very important property, some famous theorems, such as the Mackey-Arens theorem, the Mackey theorem, the Mazur theorem and the Orlicz-Pettis theorem, all show some duality invariants.

In this paper we would like to show an important improvement of the invariant results, which are related to sequential evaluation convergence of function series. Especially, a very general invariant result is established for an abstract mapping pair (Φ, B(Φ, X)) consisting of a nonempty set Φ and B(Φ, X) = {f ∈ XΦ: f (Φ) is bounded}, where X is a locally convex space.

Keywords

radiative operatorduality invariantc0-decomposability

MSC classification

Secondary: 46A63: Topological invariants ((DN), ($Omega$), etc.) 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 3 , June 2004 , pp. 369 - 382
Copyright
Copyright © Australian Mathematical Society 2004

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