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Sums and Extensions of Vector Lattice Homomorphisms

In: Positive Operators and Semigroups on Banach Lattices

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  • S. J. Bernau

    (The University of Texas at El Paso, Department of Mathematical Sciences)

Abstract

This paper gives a summary account, with minimal or no proofs, first of some results which characterize order bounded linear operators which are sums of lattice homomorphisms, or more generally of orthomorphisms; and secondly of theorems concerning extensions of vector lattice homomorphisms (theorems of Hahn—Banach type if you will). In all cases we assume that domain and range are vector lattices and that the range is Dedekind complete. The results vary from historical (pre-1940) to recent (1990). The most recent work, on sums of lattice homomorphisms, is covered in §1 and the more classical work on extension theorems is dealt with in §2.

Suggested Citation

  • S. J. Bernau, 1992. "Sums and Extensions of Vector Lattice Homomorphisms," Springer Books, in: C. B. Huijsmans & W. A. J. Luxemburg (ed.), Positive Operators and Semigroups on Banach Lattices, pages 33-45, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2721-1_4
    DOI: 10.1007/978-94-017-2721-1_4
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