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Generalized functional calculus in lattice-ordered algebras

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Abstract

We construct a functional calculus on unital uniformly complete f-algebras for continuous center-valued functions of polynomial growth and study the connection with the Minkowski duality.

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References

  1. Kusraev A. G., Homogeneous Functional Calculus on Vector Lattices, Institute of Appl. Math. Informatics VSC RAS, Vladikavkaz (2008).

    Google Scholar 

  2. Tasoev B. B., “Generalized functional calculus in vector lattices,” Vladikavkazsk. Mat. Zh., 15, No. 3, 77–88 (2013).

    MATH  Google Scholar 

  3. Buskes, G., de Pagter. B., and van Rooij A., “Functional calculus on Riesz spaces,” Indag. Math., 4, No. 2, 423–436 (1991).

    Article  Google Scholar 

  4. Haydon R., Levy M., and Raynaud Y., Randomly Normed Spaces, Hermann, Paris (1991).

    MATH  Google Scholar 

  5. Lindenstrauss J. and Tzafriri L., Classical Banach Spaces. Vol. 2: Function Spaces, Springer-Verlag, Berlin (1979).

    Book  Google Scholar 

  6. Abramovich Y. A. and Aliprantis C. D., Problems in Operators Theory, Amer. Math. Soc., Providence, RI (2002).

    Google Scholar 

  7. Aliprantis C. D. and Burkinshaw O., Positive Operators, Acad. Press, New York (1985).

    MATH  Google Scholar 

  8. Zaanen A. C., Riesz Spaces. Vol. 2, North-Holland, Amsterdam etc. (1983).

    Google Scholar 

  9. Conway J. B., A Course in Functional Analysis, Springer-Verlag, New York (1990).

    MATH  Google Scholar 

  10. Luxemburg W. A. J. and Zaanen A. C., Riesz Spaces. Vol. 1, North-Holland, Amsterdam and London (1971).

    Google Scholar 

  11. Kutateladze S. S. and Rubinov A. M., Minkowski Duality and Its Applications [in Russian], Nauka, Novosibirsk (1976).

    Google Scholar 

  12. Kusraev A. G. and Kutateladze S. S., “Envelopes and inequalities in vector lattices,” Positivity, 15, No. 4, 661–676

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Authors and Affiliations

  1. Southern Mathematical Institute, Vladikavkaz, Russia

    B. B. Tasoev

Authors
  1. B. B. Tasoev
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Correspondence to B. B. Tasoev.

Additional information

Original Russian Text Copyright © 2014 Tasoev B.B.

The author was supported by the Russian Foundation for Basic Research (Grant 12-01-00623-a).

To Yu. G. Reshetnyak on the occasion of his 85th birthday.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 5, pp. 1184–1194, September–October, 2014.

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Tasoev, B.B. Generalized functional calculus in lattice-ordered algebras. Sib Math J 55, 968–976 (2014). https://doi.org/10.1134/S0037446614050152

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  • DOI: https://doi.org/10.1134/S0037446614050152

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