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Rotundity in Lebesgue-Bochner function spaces. (English) Zbl 0368.46039


MSC:

46E40 Spaces of vector- and operator-valued functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B99 Normed linear spaces and Banach spaces; Banach lattices
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[1] K. W. Anderson, Midpoint local uniform convexity, and other geometric properties of Banach spaces, Dissertation, University of Illinois, 1960.
[2] Anatole Beck, A convexity condition in Banach spaces and the strong law of large numbers, Proc. Amer. Math. Soc. 13 (1962), 329 – 334. · Zbl 0108.31401
[3] S. Bochner and A. E. Taylor, Linear functionals on certain spaces of abstractly-valued functions, Ann. of Math. (2) 39 (1938), no. 4, 913 – 944. · Zbl 0020.37101
[4] Mahlon M. Day, Some more uniformly convex spaces, Bull. Amer. Math. Soc. 47 (1941), 504 – 507. · Zbl 0027.11003
[5] Mahlon M. Day, Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc. 78 (1955), 516 – 528. · Zbl 0068.09101
[6] Mahlon M. Day, Normed linear spaces, 3rd ed., Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 21. · Zbl 0268.46013
[7] J. Diestel and J. J. Uhl Jr., Vector measures, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. · Zbl 0369.46039
[8] A. L. Garkavi, On the optimal net and best cross-section of a set in a normed space, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 87 – 106 (Russian). · Zbl 0108.10801
[9] Daniel P. Giesy, On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc. 125 (1966), 114 – 146. · Zbl 0183.13204
[10] Robert C. James, Uniformly non-square Banach spaces, Ann. of Math. (2) 80 (1964), 542 – 550. · Zbl 0132.08902
[11] I. E. Leonard, Banach sequence spaces, J. Math. Anal. Appl. 54 (1976), no. 1, 245 – 265. · Zbl 0343.46010
[12] I. E. Leonard and K. Sundaresan, Geometry of Lebesgue-Bochner function spaces — smoothness, Bull. Amer. Math. Soc. 79 (1973), 546 – 549. · Zbl 0257.46023
[13] A. R. Lovaglia, Locally uniformly convex Banach spaces, Trans. Amer. Math. Soc. 78 (1955), 225 – 238. · Zbl 0064.35601
[14] E. J. McShane, Linear functionals on certain Banach spaces, Proc. Amer. Math. Soc. 1 (1950), 402 – 408. · Zbl 0039.11802
[15] J. Radon, Theorie und Anwendungen der absolut additiven Mengen funktionen, Sitzungsber. Akad. Wiss. Wien 122 (1913), 1295-1438. · JFM 44.0464.03
[16] F. Riesz, Sur la convergence en moyenne. I, II, Acta Sci. Math. (Szeged) 4 (1928-1929), 58-64, 182-185. · JFM 54.0282.01
[17] Haskell P. Rosenthal, Some applications of \?-summing operators to Banach space theory, Studia Math. 58 (1976), no. 1, 21 – 43. · Zbl 0339.46008
[18] Mark A. Smith, Products of Banach spaces that are uniformly rotund in every direction, Pacific J. Math. 70 (1977), no. 1, 215 – 219. · Zbl 0373.46032
[19] Mark A. Smith, Some examples concerning rotundity in Banach spaces, Math. Ann. 233 (1978), no. 2, 155 – 161. · Zbl 0391.46014
[20] V. Šmulian, Sur la dérivabilité de la norme dans l’espace de Banach, C. R. (Doklady) Acad. Sci. URSS (N. S.) 27 (1940), 643 – 648 (French). · Zbl 0023.32604
[21] Kondagunta Sundaresan, Uniformly non-\?_{\?}\?\textonesuperior \? Orlicz spaces, Israel J. Math. 3 (1965), 139 – 146. · Zbl 0146.36904
[22] Kondagunta Sundaresan, Uniformly non-square Orlicz spaces, Nieuw Arch. Wisk. (3) 14 (1966), 31 – 39. · Zbl 0151.17803
[23] Kondagunta Sundaresan, The Radon-Nikodým theorem for Lebesgue-Bochner function spaces, J. Functional Analysis 24 (1977), no. 3, 276 – 279. · Zbl 0341.46019
[24] Barry Turett and J. J. Uhl Jr., \?_{\?}(\?,\?) (1<\?<\infty ) has the Radon-Nikodým property if \? does by martingales, Proc. Amer. Math. Soc. 61 (1976), no. 2, 347 – 350. · Zbl 0349.46038
[25] V. Zizler, On some rotundity and smoothness properties of Banach spaces, Dissertationes Math. Rozprawy Mat. 87 (1971), 33 pp. (errata insert). · Zbl 0231.46036
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