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Rendiconti del Circolo Matematico di Palermo

, Volume 38, Issue 1, pp 130–139 | Cite as

Hereditary order convexity inL(X,Y)

  • N. Hadjisavvas
  • D. Kravvaritis
  • G. Pantelidis
  • I. Polyrakis
Article

Abstract

LetX be a topological vector space,Y an ordered topological vector space andL(X,Y) the space of all linear and continuous mappings fromX intoY. The hereditary order-convex cover [K] h of a subsetK ofL(X,Y) is defined by [K] h ={AL(X,Y):Ax∈[Kx] for allxX}, where[Kx] is the order-convex ofKx. In this paper we study the hereditary order-convex cover of a subset ofL(X,Y). We show how this cover can be constructed in specific cases and investigate its structural and topological properties. Our results extend to the spaceL(X,Y) some of the known properties of the convex hull of subsets ofX *.

Keywords

Compact Subset Topological Property Monotone Operator Topological Vector Space Order Vector Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Hadjisavvas N., Kravvaritis D., Pantelidis G., Polyrakis I.,Nonlinear monotone operators with values in L(X,Y), J. Math. Anal. Appl. (to appear).Google Scholar
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Copyright information

© Springer 1989

Authors and Affiliations

  • N. Hadjisavvas
    • 1
  • D. Kravvaritis
    • 1
  • G. Pantelidis
    • 1
  • I. Polyrakis
    • 1
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece

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