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Distance geometry in quasihypermetric spaces. II

Journal Article


Abstract


  • Let (X, d) be a compact metric space and let M(X ) denote the space of all finite signed Borel measures on X . Define I : M(X ) → R by I (µ) = X X d(x, y ) dµ(x) dµ(y ), and set M (X ) = sup I (µ), where µ ranges over the collection of signed measures in M(X ) of total mass 1. This paper, with an earlier and a subsequent paper [Peter Nickolas and Reinhard Wolf, Distance geometry in quasihypermetric spaces. I and III], investigates the geometric constant M (X ) and its relationship to the metric properties of X and the functional-analytic properties of a certain subspace of M(X ) when equipped with a natural semi-inner product. Using the work of the earlier paper, this paper explores measures which attain the supremum defining M (X ), sequences of measures which approximate the supremum when the supremum is not attained and conditions implying or equivalent to the finiteness of M (X ).

Publication Date


  • 2011

Citation


  • Nickolas, P. & Wolf, R. (2011). Distance geometry in quasihypermetric spaces. II. Mathematische Nachrichten, 284 (2-3), 332-341.

Scopus Eid


  • 2-s2.0-79951800942

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3566

Has Global Citation Frequency


Number Of Pages


  • 9

Start Page


  • 332

End Page


  • 341

Volume


  • 284

Issue


  • 2-3

Place Of Publication


  • Germany

Abstract


  • Let (X, d) be a compact metric space and let M(X ) denote the space of all finite signed Borel measures on X . Define I : M(X ) → R by I (µ) = X X d(x, y ) dµ(x) dµ(y ), and set M (X ) = sup I (µ), where µ ranges over the collection of signed measures in M(X ) of total mass 1. This paper, with an earlier and a subsequent paper [Peter Nickolas and Reinhard Wolf, Distance geometry in quasihypermetric spaces. I and III], investigates the geometric constant M (X ) and its relationship to the metric properties of X and the functional-analytic properties of a certain subspace of M(X ) when equipped with a natural semi-inner product. Using the work of the earlier paper, this paper explores measures which attain the supremum defining M (X ), sequences of measures which approximate the supremum when the supremum is not attained and conditions implying or equivalent to the finiteness of M (X ).

Publication Date


  • 2011

Citation


  • Nickolas, P. & Wolf, R. (2011). Distance geometry in quasihypermetric spaces. II. Mathematische Nachrichten, 284 (2-3), 332-341.

Scopus Eid


  • 2-s2.0-79951800942

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3566

Has Global Citation Frequency


Number Of Pages


  • 9

Start Page


  • 332

End Page


  • 341

Volume


  • 284

Issue


  • 2-3

Place Of Publication


  • Germany