Hiroshima Mathematical Journal

Riesz's lemma and orthogonality in normed spaces

Kazuo Hashimoto, Gen Nakamura, and Shinnosuke Oharu
Source: Hiroshima Math. J. Volume 16, Number 2 (1986), 279-304.
First Page: Show Hide
Primary Subjects: 46B20
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.hmj/1206130429
Mathematical Reviews number (MathSciNet): MR855159
Zentralblatt MATH identifier: 0606.46012

References

[1] R.G. Bilyeu andP.W.Lewis, Orthogonality andHewitt-Yosida theorem in spaces of measures, Rocky Mountain J. Math., 7 (1977), 629-638.
Zentralblatt MATH: 0375.46041
Mathematical Reviews (MathSciNet): MR450499
[2] G. Birkhor, Orthogonality inlinear metric spaces, Duke Math. J.,1 (1935), 169-172.
Zentralblatt MATH: 0012.30604
Mathematical Reviews (MathSciNet): MR1545873
[3] E. Bishiop and R.R.Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc, 67(1961), 97-98.
Zentralblatt MATH: 0098.07905
Mathematical Reviews (MathSciNet): MR123174
[4] E. Bishop and R.R.Phelps, The support functionals of a convex set, Proc. Symposia in Pure Math. (Convexity) AMS, 7 (1963), 27-35.
Zentralblatt MATH: 0149.08601
Mathematical Reviews (MathSciNet): MR154092
[5] B. Bollobas, An extension to thetheorem of Bishop and Phelps, Bull. London Math. Soc, 2 (1970), 181-182.
Zentralblatt MATH: 0217.45104
Mathematical Reviews (MathSciNet): MR267380
[6] J. Diestel, Geometry of Banach Spaces-Selected Topics, Lect. Notes in Math.,485, Springer, 1975.
Zentralblatt MATH: 0307.46009
Mathematical Reviews (MathSciNet): MR461094
[7] J. Diestel, Sequences and Series inBanach Spaces, Springer, 1984.
Zentralblatt MATH: 0542.46007
Mathematical Reviews (MathSciNet): MR737004
[8] G. Godefroy, Etude des projections de norme 1 de £ ' sur E. Unicite de certains preduaux. Applications, Ann. Inst. Fourier, Grenoble, 29(4), (1979), 53-70.
Zentralblatt MATH: 0403.46027
Mathematical Reviews (MathSciNet): MR558588
[9] I. Hada, K. Hashimoto and S.Oharu, Onthe duality mapping of £°°, Tokyo J. Math., 2 (1979), 71-97.
Zentralblatt MATH: 0417.46008
Mathematical Reviews (MathSciNet): MR541898
[10] R.C.James, Orthogonality and linear functionals in normecl linear spaces, Trans. Amer. Math. Soc, 61(1947), 265-292.
Zentralblatt MATH: 0037.08001
Mathematical Reviews (MathSciNet): MR21241
[11] R.C. James, Characterizations of reflexivity, Studia Math. 23(1964), 205-216.
Zentralblatt MATH: 0113.09303
Mathematical Reviews (MathSciNet): MR170192
[12] R. C. James, A counterexample for a sup theorem in normed spaces, Israel J.Math., 9(1971), 511-512.
Zentralblatt MATH: 0211.14901
Mathematical Reviews (MathSciNet): MR279565
[13] S. Katutani, Concrete representation of abstract (L )-spaces and mean ergodic theorem, Ann. of Math., 42(1941), 523-537.
Zentralblatt MATH: 0027.11102
Mathematical Reviews (MathSciNet): MR4095
[14] S. Kakutani, Concrete representation of abstract (M)-spaces, Ann. of Math., 42 (1941), 994-1024.
Zentralblatt MATH: 0060.26604
Mathematical Reviews (MathSciNet): MR5778
[15] M. Schechter, Principles of Functional Analysis, Academic Press, 1973.
Zentralblatt MATH: 0211.14501
Mathematical Reviews (MathSciNet): MR445263
[16] I. Singer, Best Approximation in Normed Linear Spaces byElements ofLinear Subspaces, Grundlehren derMath. Wiss., 171, Springer, 1970.
Zentralblatt MATH: 0197.38601
[17] A. E. Taylor, Introduction toFunctional Analysis, Wiley, 1958.
Zentralblatt MATH: 0081.10202
Mathematical Reviews (MathSciNet): MR98966
[18] K.Yosida and E.Hewitt, Finitely additive measures, Trans. Amer. Math. Soc, 72 (1952), 46-66.
Zentralblatt MATH: 0046.05401
Mathematical Reviews (MathSciNet): MR45194

2013 © Hiroshima University, Department of Mathematics

Hiroshima Mathematical Journal

Hiroshima Mathematical Journal