×

zbMATH — the first resource for mathematics

The geometry of Banach spaces. Smoothness. (English) Zbl 0123.30701

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] W. Anderson 1. Midpoint local uniform convexity, and other geometric properties of Banach spaces Doctoral dissertation, Univ. of Illinois, Urbana, Illinois, 1960, 48 pp.
[2] Guido Ascoli, Sugli spazi lineari metrici e le loro varietà lineari, Ann. Mat. Pura Appl. 10 (1932), no. 1, 33 – 81 (Italian). · Zbl 0003.40902 · doi:10.1007/BF02417133 · doi.org
[3] Errett Bishop and R. R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67 (1961), 97 – 98. · Zbl 0098.07905
[4] H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere of Banach algebras, Ann. of Math. (2) 62 (1955), 217 – 229. · Zbl 0067.35002 · doi:10.2307/1969676 · doi.org
[5] Herbert Busemann, Convex surfaces, Interscience Tracts in Pure and Applied Mathematics, no. 6, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. · Zbl 0087.36201
[6] James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396 – 414. · Zbl 0015.35604
[7] D. F. Cudia, Rotundity, Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 1963, pp. 73 – 97. · Zbl 0141.11901
[8] Mahlon M. Day, Uniform convexity in factor and conjugate spaces, Ann. of Math. (2) 45 (1944), 375 – 385. · Zbl 0063.01058 · doi:10.2307/1969275 · doi.org
[9] Mahlon M. Day, Strict convexity and smoothness of normed spaces, Trans. Amer. Math. Soc. 78 (1955), 516 – 528. · Zbl 0068.09101
[10] Mahlon M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. Heft 21. Reihe: Reelle Funktionen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. · Zbl 0082.10603
[11] Ky Fan and Irving Glicksberg, Fully convex normed linear spaces, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 947 – 953. · Zbl 0065.34501
[12] Ky Fan and Irving Glicksberg, Some geometric properties of the spheres in a normed linear space, Duke Math. J. 25 (1958), 553 – 568. · Zbl 0084.33101
[13] Robert C. James, Reflexivity and the supremum of linear functionals, Ann. of Math. (2) 66 (1957), 159 – 169. · Zbl 0079.12704 · doi:10.2307/1970122 · doi.org
[14] R. C. James, Characterizations of reflexivity, Studia Math. 23 (1963/1964), 205 – 216. · Zbl 0113.09303
[15] V. L. Klee Jr., Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc. 3 (1952), 484 – 487. · Zbl 0047.02902
[16] Victor L. Klee Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10 – 43. · Zbl 0050.33202
[17] Victor Klee, Some new results on smoothness and rotundity in normed linear spaces., Math. Ann. 139 (1959), 51 – 63 (1959). · Zbl 0092.11602 · doi:10.1007/BF01459822 · doi.org
[18] M. A. Krasnosel\(^{\prime}\)skiĭ and Ja. B. Rutickiĭ, Convex functions and Orlicz spaces, Translated from the first Russian edition by Leo F. Boron, P. Noordhoff Ltd., Groningen, 1961.
[19] A. R. Lovaglia, Locally uniformly convex Banach spaces, Trans. Amer. Math. Soc. 78 (1955), 225 – 238. · Zbl 0064.35601
[20] Mazur 1. Über konvexe Mengen in linearen normierten Räumen, Studia Math. 4 (1933), 70-84. · JFM 59.1074.01
[21] A. F. Ruston, A note on convexity in Banach spaces, Proc. Cambridge Philos. Soc. 45 (1949), 157 – 159. · Zbl 0031.31201
[22] V. Šmulian, On some geometrical properties of the sphere in a space of type (B), C. R. (Doklady) Acad. Sci. URSS (N. S.) 24 (1939), 648 – 652. · Zbl 0022.14903
[23] V. Šmulian, On some geometrical properties of the unit sphere in the space of the type (B), Rec. Math. N. S. [Mat. Sbornik] 6(48) (1939), 77 – 94 (Russian, with English summary). · JFM 66.1283.02
[24] 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
[25] V. L. Šmulian, Sur la structure de la sphère unitaire dans l’espace de Banach, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 545 – 561 (French). · JFM 67.0400.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.