Nonstandard hulls of lattice-normed ordered vector spaces

Authors : Abdullah Aydin, Svetlana Gorokhova, Hasan Gül

Pages : 155-163

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach--Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.
Keywords : Vector lattice, ordered vector space, lattice-normed space, decomposable lattice norm, associated Banach--Kantorovich space, lattice-normed ordered vector space, nonstandard hull