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Separation by semidefinite bilinear forms

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General Inequalities 7

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 123))

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Abstract

In this paper we offer necessary and sufficient conditions on the separability of two given functions by nonnegative definite symmetric bilinear forms. As a consequence, we characterize those functions that are pointwise suprema of symmetric nonnegative definite bilinear functions and also those set-valued functions that are generated by nonnegative selfadjoint operators.

Research supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T-016846.

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References

  1. Zs. Páles, Linear selections for set-valued functions and extension of bilinear forms, Arch. Math., 62 (1994), 427–432.

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  2. Zs. Páles, Separation with symmetric bilinear forms and symmetric selections of set-valued functions, Publ. Math. Debrecen, 46 (1995), 321–331.

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  3. Zs. Páles and V. Zeidan, Generalized Hessian for C 1,1 functions in infinite dimensional normed spaces, Math. Programming, to appear.

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  4. Zs. Páles and V. Zeidan, Separation via quadratic functions, Aequationes Math., to appear.

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  5. B. Rodrigues-Salinas and L. Bou, A Hahn-Banach theorem for arbitrary vector spaces, Boll. Un. Math. Ital. (4)10 (1974), 390–393.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, L. Kossuth University, H-4010, Debrecen, Pf. 12, Hungary

    Zsolt Páles

Authors
  1. Zsolt Páles
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, University of Basel, Rheinsprung 21, 4051, Basel, Switzerland

    Catherine Bandle

  2. School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, England, UK

    William N. Everitt

  3. Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, 13060, Safat, Kuwait

    Laszlo Losonczi

  4. Institue of Mathematics I, University of Karlsruhe, Kaiserstr. 12, 76128, Karlsruhe, Germany

    Wolfgang Walter

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© 1997 Springer Basel AG

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Páles, Z. (1997). Separation by semidefinite bilinear forms. In: Bandle, C., Everitt, W.N., Losonczi, L., Walter, W. (eds) General Inequalities 7. ISNM International Series of Numerical Mathematics, vol 123. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8942-1_21

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  • DOI: https://doi.org/10.1007/978-3-0348-8942-1_21

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9837-9

  • Online ISBN: 978-3-0348-8942-1

  • eBook Packages: Springer Book Archive

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