Abstract
In this article, we study the convergence of sequences of operators on some classical vector-valued sequence spaces in the frame of abstract dual systems. Several consequences of full invariants are obtained.
Highlights
1 Introduction A dual system in linear analysis consists of a linear space and a collection of linear functionals defined on the linear space
Theory of locally convex spaces is exactly about theory of dual systems which plays a crucial role in many fields of mathematical analysis
Many people working in different fields of mathematics have been devoting themselves on the research of some special dual systems such as measure system (Σ,Ca(Σ,X)), abstract function system (Ω,C(Ω,X)) and operator system (X,L(X,Y)) as well as fuzzy system (U,F(U)) etc
Summary
A dual system in linear analysis consists of a linear space and a collection of linear functionals defined on the linear space. The purpose of this article is to study full invariant of the convergence in (Ylp(X), lp(X))-topology on the dual system (Ylp(X), lp(X)), (0 < p ≤ ∞). If b(X, Y) ⊇ s (X, Y), b(X, Y) is called an admissible polar topology on X with respect to the dual system (X,Y).
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