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Some parameters of Banach spaces

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Si passano in rassegna varie proprietà di alcune costanti, introdotte nello studio della geometria della palla unitaria in uno spazio di Banach. Si mettono in relazione vari risultati su di esse publicati di recente, in parte anche su periodici cinesi.

Summary

We review several properties of some constants considered in the study of the geometry of Banach spaces. We relate many results on them published recently, partly also on chinese journals.

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References

  1. Amir D., Franchetti C.,The radius ratio and convexity properties in normed linear spaces. Trans. Amer. Math. Soc., 282 (1984), 275–291.

    Article  MathSciNet  MATH  Google Scholar 

  2. Betts J. R., Thompson A. C.,Three remarks on the measurement of unit spheres. Canad. Math. Bull. 18 (1975), 485–488.

    MathSciNet  MATH  Google Scholar 

  3. Bos A.,Sphere-packings in euclidean space. Packing and covering in combinatorics (Study week, Amsterdam 1978), 2nd Ed., ed. by A. Schrijver, Math. Centre Tracts 106, Amsterdam 1982, 161–177.

  4. Bronshteîn E. M.,ε-entropy of convex sets and functions. Siberian Math. J. 17 (1976), 393–398.

    Article  Google Scholar 

  5. Brown D. R.,P-convexity and B-convexity in Banach spaces Trans. Amer. Math. Soc. 187 (1974), 77–81.

    Article  MathSciNet  MATH  Google Scholar 

  6. Buî-Min-Cî, Gurariî V. I.,Some characteristic of normed spaces and their application to generalize to Banach spaces Parseval equality (Russian). Teor. Funkciî Funkcional. Anal. i Prilozên., Vyp. 8 (1969), 74–91.

    Google Scholar 

  7. Burlak J. A. C., Rankin R. A., Robertson A. P.,The packing of spheres in the space l p. Proc. Glascow Math. Assoc. 4 (1959), 22–25.

    Article  MathSciNet  Google Scholar 

  8. Bynum W. L.,Characterizations of uniform convexity Pacific J. Math. 38 (1971), 577–581.

    MathSciNet  MATH  Google Scholar 

  9. Casazza P. G.,Tsirelson’s space. Proceedings of a Research Workshop on Banach space theory, ed. by Bor-Luh Lin, Univ. of Iowa 1981 (1982), 9–22.

  10. Cleaver C. E.,Packing spheres in Orlicz spaces. Pacific J. Math. 65 (1976) 325–335.

    MathSciNet  MATH  Google Scholar 

  11. Daneš J.,On the Istrâţescu’s measure of noncompactness Bull. Math. Soc. Sci. Math. R. S. Roumanie 16 (64) (1972), 403–406.

    MathSciNet  Google Scholar 

  12. Elton J., Odell E.,The unit ball of every infinite-dimensional normed linear space contains a (1+ε)-separated sequence. Colloq. Math. 44 (1981), 105–109.

    MathSciNet  MATH  Google Scholar 

  13. Fejes Tóth G.,New results in the theory of packing and covering. Convexity and its applications, ed. by P. M. Gruber and J. M. Wills, Birkhäuser Verlag, Basel 1983, 318–359.

    Google Scholar 

  14. Fejes Tóth L.,Lagerungen in der Ebene, auf der Kugel und im Raum. 2nd Ed., Grundl. Math. Wiss. 65, Springer-Verlag, Berlin-Heidelberg-New York, 1972.

    MATH  Google Scholar 

  15. Gao J.,Several relations of packing in a Banach space (Chinese, English summary). Nanjing Daxue Xuebao 1981, no 2, 189–196.

    Google Scholar 

  16. Gao J.,The extreme value of the uniform degree of the unit ball of a Banach space (Chinese, English summary). Nanjing Daxue Xuebao 1983, no 1, 5–12.

    Google Scholar 

  17. Gao J.,The uniform degree of the unit ball of Banach space (I) (Chinese, English summary). Nanjing Daxue Xuebao 1982, no 1, 14–28.

    Google Scholar 

  18. Gastinel N., Joly J. L.,Condition numbers and general projection method. Linear Algebra Appl. 3 (1970), 185–224.

    Article  MathSciNet  MATH  Google Scholar 

  19. Giel C., Cleaver C.,Packing spheres in C p spaces Studia Math. 72 (1982), 1–8.

    MathSciNet  MATH  Google Scholar 

  20. Istraţescu V. I.,On a measure of noncompactness. Bull. Math. Soc. Sci. Math. R. S. Roumanie 16 (64) (1972), 195–197.

    MathSciNet  Google Scholar 

  21. Klee V.,Dispersed Chebyshev sets and covering by balls Math. Ann. 257 (1981), 251–260.

    Article  MathSciNet  MATH  Google Scholar 

  22. Kolmogorov A. N., Tihomirov V. M.,ε-entropy and ε-capacity of sets in functional spaces (Russian). Uspehi Mat. Nauk 14 no 2 (1959), 3–86; English transl.: Amer. Math. Soc. Transl. (2) 17 (1961), 277–364.

    MathSciNet  MATH  Google Scholar 

  23. Kottmann C. A.,Packing and reflexivity in Banach spaces. Trans. Amer. Math. Soc. 150 (1970), 565–576.

    Article  MathSciNet  Google Scholar 

  24. Kottmann C. A.,Subsets of the unit ball that are separated by more than one. Studia Math. 53 (1975), 15–27.

    MathSciNet  Google Scholar 

  25. Larman D. G., Rogers C. A.,Durham symposium on the relations between infinite-dimensional and finite-dimensional convexity. Bull. London Math. Soc. 8 (1976), 1–33.

    Article  MathSciNet  MATH  Google Scholar 

  26. Lorentz G. G.,Metric entropy and approximation. Bull. Amer. Math. Soc. 72 (1966), 903–937.

    Article  MathSciNet  MATH  Google Scholar 

  27. Naidu S. V. R., Sastry K. P. R.,Convexity conditions in normed linear spaces. J. Reine Angew. Math. 297 (1978), 35–53.

    MathSciNet  MATH  Google Scholar 

  28. Papini P. L.,Some questions related to the concept of orthogonality in Banach spaces. Proximity maps; bases. Boll. Un. Mat. Ital., (4) 11 (1975), 44–63.

    MathSciNet  MATH  Google Scholar 

  29. Rankin R. A.,On packing of spheres in Hilbert space. Proc. Glascow Math. Assoc. 2 (1955), 145–146.

    MathSciNet  MATH  Google Scholar 

  30. Schäffer J. J.,Geometry of spheres in normed spaces. Lecture Notes in Pure and Appl. Math. 20, M. Dekker, New York, 1976.

    MATH  Google Scholar 

  31. Singer I.,Bases in Banach spaces I. Grundl. Math. Wiss. 154, Springer-Verlag, Berlin-Heidelberg-New York 1970.

    MATH  Google Scholar 

  32. Singer I.,Bases in Banach spaces II. Springer-Verlag, Berlin-Heidelberg-New York, 1981.

    MATH  Google Scholar 

  33. Spence E.,Packing of spheres in l p. Glascow Math. J. 11 (1970), 72–80.

    MathSciNet  MATH  Google Scholar 

  34. Wells, J. H., Williams L. R.,Embeddings and extensions in analysis. Ergebn. Math. 84, Springer-Verlag, Berlin-Heidelberg-New York, 1975.

    MATH  Google Scholar 

  35. Whitley R.,The size of the unit sphere. Canad. J. Math. 20 (1968), 450–455.

    MathSciNet  MATH  Google Scholar 

  36. Yin H.,About three geometric parameters of normed linear spaces (Chinese, English summary). J. Math. Res. Exposition 1981, no 2, 39–48.

    Google Scholar 

  37. Yin H.,On the Kottmann problem (Chinese, English summary). Chinese Ann. Math. 3 (1982), 617–623.

    MathSciNet  MATH  Google Scholar 

  38. Yin H.-S., Zhao J.-F., Wang C.-H.,On λ-separated subsets of unit spheres of normed linear spaces (Chinese, English summary). Nanjing Daxue Xuebao 1980 (Science Report of Nanjing Univ., Special Issue on Math.), 123–129.

  39. Zhao J.-F., Wang C.-H., Ying H.-S.,On some properties of flat Banach spaces. J. of Mathematics 1 (1981), 96–100.

    MathSciNet  MATH  Google Scholar 

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(Conferenza tenuta il 26 ottobre 1983)

Work performed under the auspices of the G.N.A.F.A. of C.N.R. (Consiglio Nazionale delle Ricerche) and of the M.P.I. (Ministero della Pubblica Istruzione).

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Papini, P.L. Some parameters of Banach spaces. Seminario Mat. e. Fis. di Milano 53, 131–148 (1983). https://doi.org/10.1007/BF02924891

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