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Compactness and Vitali’s compactness criterion in vector-valued F-seminormed function spaces

  • Marianna Tavernise
  • Alessandro Trombetta
  • Giulio Trombetta
Article
  • 16 Downloads

Abstract

Results of compactness for vector-valued F-seminormed function spaces and a general Vitali’s compactness criterion under the W-property are exhibited.

Keywords

Hausdorff measure of noncompactness Measure of non equiabsolute continuity Vector-valued F-seminormed function space W-property 

Mathematics Subject Classification

47H08 46E40 

References

  1. 1.
    Avallone, A.: Spaces of measurable functions I. Ricerche Mat. 39(2), 221–246 (1990)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Avallone, A.: Spaces of measurable functions II. Ricerche Mat. 41(1), 3–19 (1991)MathSciNetzbMATHGoogle Scholar
  3. 4.
    Avallone, A., Trombetta, G.: Measures of noncompactness in the space \(L_{0}\) and a generalization of the Arzelà-Ascoli theorem. Boll. Un. Mat. Ital. 7(3), 573–587 (1991)zbMATHGoogle Scholar
  4. 5.
    Diaz, S., Mayoral, F.: On compactness in spaces of Bochner integrable functions. Acta Mat. Hung. 83(3), 231–239 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 6.
    De Lucia, P., Weber, H.: Completeness of function spaces. Ricerche Mat. 39(1), 81–97 (1990)MathSciNetzbMATHGoogle Scholar
  6. 7.
    Dunford, N., Schwartz, J.T.: Linear Operators: Part I. Wiley, New York (1958)zbMATHGoogle Scholar
  7. 8.
    Jarchow, H.: Locally Convex Spaces. B. G. Teubner, Stuttgart (1981)CrossRefzbMATHGoogle Scholar
  8. 11.
    Keim, D.: Die ordnungstopologie und ordnungstonnelierte topologien auf vektorverbanden. Collect. Math. 22, 117–140 (1971)MathSciNetzbMATHGoogle Scholar
  9. 12.
    Lepellere, M.A., Trombetta, G.: On some measures of noncompactness and the measure of non equiabsolute continuity in function spaces. Ricerche Mat. 46(2), 291–306 (1997)MathSciNetzbMATHGoogle Scholar
  10. 13.
    Musielak, J.: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics. Springer, Berlin (1983)CrossRefzbMATHGoogle Scholar
  11. 14.
    Neerven, J.V.: Compactness in vector-valued Banach function spaces. Positivity 11(3), 461–467 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 15.
    Simon, J.: Compact sets in the space \(L^p(0, T;B)\). Ann. Mat. Pura Appl. 146(4), 65–96 (1987)MathSciNetzbMATHGoogle Scholar
  13. 16.
    Tavernise, M., Trombetta, A., Trombetta, G.: Total boundedness in vector-valued \(F\)-seminormed function spaces. Matematiche (Catania) 66(1), 171–179 (2011)MathSciNetzbMATHGoogle Scholar
  14. 18.
    Uhl Jr., J.J.: Orlicz spaces of finitely additive set functions. Studia Math. 29, 19–58 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 19.
    Vath, M.: Ideal Spaces. Lecture Notes in Mathematics. Springer, Berlin (1997)Google Scholar
  16. 20.
    Vath, M.: A compactness criterion of mixed Krasnoselskiǐ–Riesz type in regular ideal spaces of vector functions. Z. Anal. Anwend. 18(3), 713–732 (1999)CrossRefzbMATHGoogle Scholar
  17. 21.
    Wong, Y.C., Ng, K.F.: Partially ordered topological vector spaces. Clarendon Press, Oxford (1973)zbMATHGoogle Scholar

Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  • Marianna Tavernise
    • 1
  • Alessandro Trombetta
    • 1
  • Giulio Trombetta
    • 1
  1. 1.Department of MathematicsUniversity of CalabriaArcavacata di RendeItaly

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