Skip to main content
Log in

Measurable bundles of Banach lattices

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

The aim of this paper is to outline a portion of the theory of liftable bundles of Banach lattices and to give some applications to representation of dominated operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aliprantis C.D., Burkinshaw O.: Positive Operators. Academic Press, London (1985)

    MATH  Google Scholar 

  2. Bukhvalov A.V.: On analytical representation of operators with abstract norm. Dokl. Akad. Nauk SSSR 208(5), 1012–1015 (1973)

    MathSciNet  Google Scholar 

  3. Bukhvalov A.V.: On analytical representation of operators with abstract norm. Isv. Vyssh. Uchebn. Zaved. Mat. 11, 21–32 (1975)

    Google Scholar 

  4. Castaing C., Valadier M.: Convex Analysis and Measurable Multifunctions. Springer, Berlin (1977)

    MATH  Google Scholar 

  5. Buskes G., de Pagter B., van Rooij A.: Functional calculus on Riesz spaces. Indag. Math. (N.S.) 4(2), 423–436 (1991)

    Article  Google Scholar 

  6. Cembranos P., Mendoza J.: Banach Spaces of Vector-Valued Functions. Springer, Berlin (1997)

    MATH  Google Scholar 

  7. Diestel, J., Uhl, J.J.: Vector Measures. In: Series of Mathematical Surveys, vol. 15. American Mathematical Society, Providence (1977)

  8. Dinculeanu N.: Vector Measures. VEB Deutscher Verlag der Wissenschaften, Berlin (1966)

    MATH  Google Scholar 

  9. Fourman, M.P., Mulvey, C.J., Scott, D.S. (eds.): Applications of Sheaves. In: Proceedings of the Research Symposium on Application of Sheaf Theory to Logic, Algebra and Analysis. University of Durham, Durham, 1977. Springer, Berlin (1979)

  10. Ganiev, I.G.: Measurable bundles of lattices and their applications. In: Studies on Functional Analysis and its Applications, pp. 9–49. Nauka, Moscow (2006)

  11. Gierz G.: Bundles of Topological Vector Spaces and their Duality. Springer, Berlin (1982)

    MATH  Google Scholar 

  12. Gutman A.E.: Banach bundles in the theory of lattice-normed spaces. I. Continuous Banach bundles. Siberian Adv. Math. 3(3), 1–55 (1993)

    MATH  MathSciNet  Google Scholar 

  13. Gutman A.E.: Banach bundles in the theory of lattice-normed spaces. II. Measurable Banach bundles. Siberian Adv. Math. 3(4), 8–40 (1993)

    MATH  MathSciNet  Google Scholar 

  14. Gutman A.E.: Banach bundles in the theory of lattice-normed spaces. III. Approximating sets and bounded operators. Siberian Adv. Math. 4(2), 54–75 (1994)

    MATH  MathSciNet  Google Scholar 

  15. Gutman, A.E.: Banach bundles in the theory of lattice-normed spaces. In: Linear Operators Compatible with Order, pp. 63–211. Sobolev Institute Press, Novosibirsk (1995) (in Russian)

  16. Hofman, K.H., Keimel, K.: Sheaf theoretical concepts in analysis: bundles and sheaves of Banach spaces, Banach C(X)-modules. In: Applications of Sheaves. Lectures Notes in Mathematics, vol. 753, pp. 415–441. Springer, Berlin (1979)

  17. Ionescu T.A., Ionescu T.C.: Topics in the Theory of Lifting. Springer, Berlin (1969)

    MATH  Google Scholar 

  18. Kusraev A.G.: Vector Duality and its Applications (in Russian). Nauka, Novosibirsk (1985)

    Google Scholar 

  19. Kusraev A.G.: Dominated Operators. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

  20. Kusraev, A.G.: Homogeneous Functional Calculus on Vector Lattices, pp. 1–34. Institute of Applied Mathematics and Information. VSC RAS, Vladikavkaz (2008)

  21. Kusraev A.G.: Functional calculus and Minkowsli duality on vector lattices. Vladikavkaz Math. J. 11(2), 31–42 (2009)

    MathSciNet  Google Scholar 

  22. Kusraev A.G., Kutateladze S.S.: Subdifferentials: Theory and Applications. Nauka, Moscow (2007)

    Google Scholar 

  23. Kusraev, A.G., Kutateladze, S.S.: Subdifferentials: Theory and Applications. Kluwer, Dordrecht (1995)

  24. Kusraev, A.G., Strizhevskiĭ, V.Z.: Lattice-normed spaces and dominated operators. In: Studies on Geometry and Functional Analysis, vol. 7, pp. 132–158. Trudy Inst. Mat., Novosibirsk (1987) (in Russian)

  25. Levin V.L.: Convex Analysis in Spaces of Measurable Functions and its Applications in Mathematics and Economics (in Russian). Nauka, Moscow (1985)

    Google Scholar 

  26. Lin P.-K.: Köthe–Bochner Functions Spaces. Birkhäuser, Boston (2004)

    Google Scholar 

  27. Lozanovskiĭ G.: The functions of elements of vector lattices. Izv. Vyssh. Uchebn. Zaved. Mat. 4, 45–54 (1973)

    Google Scholar 

  28. Meyer-Nieberg P.: Banach Lattices. Springer, Berlin (1991)

    MATH  Google Scholar 

  29. Schochetman I.E.: Kernels and Integral Operators for Continuous Sums of Banach Spaces. American Mathematical Society, Providence (1978)

    Google Scholar 

  30. von Neumann J.: On rings of operators. III. Ann. Math. 41, 94–161 (1940)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. G. Kusraev.

Additional information

This article was supported by a grant from Russian Foundation for Basic Research, project no. 09-01-00442.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kusraev, A.G. Measurable bundles of Banach lattices. Positivity 14, 785–799 (2010). https://doi.org/10.1007/s11117-010-0063-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11117-010-0063-y

Keywords

Mathematics Subject Classification (2000)

Navigation