Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Benyamini, The uniform classification of Banach spaces, Longhorn notes, University of Texas 1984–85.
B. Beauzamy, Introduction to Banach spaces and their goemetry, North Holland Mathematical Studies 68, sectond edition, 1985.
R.D. Bourgin, Geometric aspects of convex sets with the Radon Nikodym Property, Springer Lecture Notes #993, 1983.
S. Banach and S. Mazur, Zur Theorie der linearen Dimension, Studia Math. 4(1933), 110–112.
C. Bessaga and A. Pelczynski, Selected topics in infinite dimensional topology, Monografie Matematyczne 58, Warsaw 1975.
E. Bishop and R.R. Phelps, The support functionals of a convex set, Proc. Symp. Pure Math. AMS 7 (1963), 27–36.
O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics I, Springer Verlag 1979.
Y. Benyamini and Y. Sternfeld, Spheres in infinite dimensional normed spaces are Lipschitz contractible, Proc. AMS 88 (1983), 439–445.
J. Diestel, Geometry of Banach spaces, selected topics, Springer Lecture Notes #485, 1975.
W. Davis, N. Ghoussoub and J. Lindenstrauss, A lattice renorming theorem and applications to vector valued processes, Trans. AMS 263 (1981), 531–540.
J. Diestel and J.J. Uhl, Vector measures, Math. Surveys 15 AMS, 1977.
P. Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math. 13 (1973), 281–288.
N. Ghoussoub and B. Maurey, H δ embeddings in Hilbert space and optimization on G δ sets, Memoirs of the AMS, #349, 1986.
R.C. James, Weakly compact sets, Trans. AMS 113 (1964), 129–140.
R.C. James, Some self dual properties of normed linear spaces, Ann. Math. Studies 69 (1972), 159–175.
V. Klee, Some topological properties of convex sets, Trans. AMS 78 (1955), 30–45.
V. Klee, Some new results on smoothness and rotundity in normed linear spaces, Math. Ann 139 (1959), 51–63.
J. Lindenstrauss, G. Olsen and Y. Sternfeld, The Poulsen simplex, Ann. Inst. Fourier 28 (1978), 91–114.
P.K. Lin and Y. Sternfeld, Convex sets with the Lipschitz fixed point property are compact, Proc. AMS 93 (1985), 633–639.
J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Vol 1, Sequence spaces, Springer Verlag 1977.
J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Vol 2, Function spaces, Springer Verlag 1979.
R.I. Ovsepian and A. Pelczynski, The existence in every separable Banach space of a fundamental total and bounded biorthogonal system. Studia Math. 54 (1975), 149–159.
A. Pelczynski, Any separable Banach space admits for every ε > 0 fundamental and total biorthogonal sequences bounded by 1 + ε. Studia Math. 55 (1976), 295–304.
R.R. Phelps, Lectures on Choquet's theorem, Van Nostrand Math. Studies 1966.
G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), 326–350.
E.T. Poulsen, A simplex with dense extreme boundary, Ann. Inst. Fourier 11 (1961), 83–87.
D. Preiss, Differentiability of Lipshcitz functions on Banach spaces (to appear).
M.M Vainberg, Some questions of differential calculus in linear spaces, Uspehi Mat. Nauk 7 (50) (1952), 55–102.
M. Zippin, Banach spaces with separable duals, (to appear in Trans. AMS).
Author information
Authors and Affiliations
Editor information
Additional information
Dedicated to the memory of D.P. Milman (1912–1982).
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Lindenstrauss, J. (1988). Some useful facts about Banach spaces. In: Lindenstrauss, J., Milman, V.D. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081740
Download citation
DOI: https://doi.org/10.1007/BFb0081740
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19353-1
Online ISBN: 978-3-540-39235-4
eBook Packages: Springer Book Archive