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On automatic boundedness of operators between ordered and topological vector spaces

Eduard Emelyanov, Svetlana Gorokhova

Abstract

We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. Levi and Lebesgue operators are investigated.

On automatic boundedness of operators between ordered and topological vector spaces

Abstract

We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. Levi and Lebesgue operators are investigated.
Paper Structure (3 sections, 23 theorems, 6 equations)

This paper contains 3 sections, 23 theorems, 6 equations.

Table of Contents

  1. Introduction and preliminaries
  2. On boundedness of some operators between ordered TVSs
  3. On boundedness of Levi and Lebesgue operators between ordered TVSs

Key Result

Proposition 2.3

(E1-2026) We have $\text{\bf L}_{o{\tau}b}(X,Y)\subseteq\text{\bf L}_{r{\tau}c}(X,Y)$, whenever $X$ is an OVS and $Y$ is a TVS. If, additionally, $X_+-X_+=X$ then $\text{\bf L}_{o{\tau}b}(X,Y)=\text{\bf L}_{r{\tau}c}(X,Y)$.

Theorems & Definitions (36)

  • Definition 2.1
  • Definition 2.2
  • Proposition 2.3
  • Proposition 2.4
  • Proposition 2.5
  • Proposition 2.6
  • Theorem 2.7
  • proof
  • Corollary 2.8
  • Corollary 2.9
  • ...and 26 more