Rocky Mountain Journal of Mathematics

Extreme and Smooth Points in Lorentz and Marcinkiewicz Spaces with Applications to Contractive Projections

Anna Kamińska, Han Ju Lee, and Grzegorz Lewicki
Source: Rocky Mountain J. Math. Volume 39, Number 5 (2009), 1533-1572.
First Page: Show Hide
Primary Subjects: 46B04, 46B20, 46B45
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1255008573
Digital Object Identifier: doi:10.1216/RMJ-2009-39-5-1533
Mathematical Reviews number (MathSciNet): MR2546654
Zentralblatt MATH identifier: 1192.46010

References

M.D. Acosta, F.J. Aguirre and R. Payá, There is no bilinear Bishop-Phelps theorem, Israel J. Math. 93 (1996), 221-227.
P. Bandyopadhyay and S. Dutta, Almost constrained subspaces of Banach spaces, Proc. Amer. Math. Soc. 132 (2004), 107-116.
Mathematical Reviews (MathSciNet): MR2021253
Zentralblatt MATH: 1050.46013
Digital Object Identifier: doi:10.1090/S0002-9939-03-07146-6
B. Beauzamy and P. Enflo, Théorèmes de point fixe et d'approximation, Ark. Mat. 23 (1985), 19-34.
Mathematical Reviews (MathSciNet): MR800172
B. Beauzamy and B. Maurey, Points minimaux et ensembles optimaux dans les espaces de Banach, J. Funct. Anal. 24 (1977), 107-139.
Mathematical Reviews (MathSciNet): MR428014
Digital Object Identifier: doi:10.1016/0022-1236(77)90049-0
Zentralblatt MATH: 0344.46049
R.E. Bruck, Jr., Properties of fixed-point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc. 179 (1973), 251-262.
Mathematical Reviews (MathSciNet): MR324491
Zentralblatt MATH: 0265.47043
Digital Object Identifier: doi:10.2307/1996502
--------, Nonexpansive projections on subsets of Banach spaces, Pacific J. Math. 47 (1973), 341-355.
Mathematical Reviews (MathSciNet): MR341223
Zentralblatt MATH: 0274.47030
Project Euclid: euclid.pjm/1102945870
N.L. Carothers and S.J. Dilworth, Geometry of Lorentz spaces via interpolation, Texas Functional Analysis Seminar 1985-1986 (Austin, TX, 1985-1986); Longhorn Notes, University of Texas, Austin, TX (1986), 107-133.
Mathematical Reviews (MathSciNet): MR1017049
Zentralblatt MATH: 0754.46023
N.L. Carothers and S.J. Dilworth, Equidistributed random variables in $L\sb p,q$, J. Functional Anal. 84 (1989), 146-159.
Mathematical Reviews (MathSciNet): MR999493
Zentralblatt MATH: 0691.46015
Digital Object Identifier: doi:10.1016/0022-1236(89)90115-8
Y.S. Choi, K.H. Han and H.G. Song, Extensions of polynomials on preduals of Lorentz sequence spaces, Glasgow Math. J. 47 (2005), 395-403.
Mathematical Reviews (MathSciNet): MR2203508
Zentralblatt MATH: 1092.46030
Digital Object Identifier: doi:10.1017/S0017089505002624
Ch. Choi, A. Kamińska and H.J. Lee, Complex convexity of Orlicz-Lorentz spaces and its applications, Bull. Pol. Acad. Sci. Math. 52 (2004), 19-38.
Mathematical Reviews (MathSciNet): MR2070025
Zentralblatt MATH: 1109.46032
Digital Object Identifier: doi:10.4064/ba52-1-3
V. Davis and P. Enflo, Contractive projections on $l_p$-spaces, London Math. Soc. Lecture Notes Series 137 (1989), 151-161.
R. Deville, G. Godefroyd and V. Zizler, Smoothness and renormings in Banach spaces, Wiley, New York, 1993.
Mathematical Reviews (MathSciNet): MR1211634
Zentralblatt MATH: 0782.46019
P. Enflo, Contractive projections onto subsets of $L^1(0,1)$, London Math. Soc. Lecture Notes Series 137 (1989), 162-184.
Mathematical Reviews (MathSciNet): MR1009174
--------, Contractive projections onto subsets of $L^p$-spaces, in Function spaces, Lecture Notes Pure Appl. Math. 136, Marcel Dekker, Inc., New York, 1992. 79--94.
W.T. Gowers, Symmetric block bases of sequences with large average growth, Israel J. Math. 69 (1990), 129-151.
Mathematical Reviews (MathSciNet): MR1045369
Zentralblatt MATH: 0721.46010
Digital Object Identifier: doi:10.1007/BF02937300
P. Harmand, D. Werner and W. Werner, $M$-ideals in Banach spaces and Banach algebras, Lecture Notes Math., 1547, Springer-Verlag, New York, 1993.
Mathematical Reviews (MathSciNet): MR1238713
Zentralblatt MATH: 0789.46011
J. Jamison, A. Kamińska and G. Lewicki, One-complemented subspaces of Musielak-Orlicz sequence spaces, J. Approx. Theory 130 (2004), 1-37.
Mathematical Reviews (MathSciNet): MR2086807
Zentralblatt MATH: 1135.46303
Digital Object Identifier: doi:10.1016/j.jat.2004.07.001
A. Kamińska and H.J. Lee, $M$-ideal properties in Marcinkiewicz spaces, Comment. Math., Special volume for 75th birthday of Julian Musielak, (2004), 123-144.
Mathematical Reviews (MathSciNet): MR2111760
A. Kamińska and G. Lewicki, Contractive and optimal sets in modular spaces, Math. Nachr. 268 (2004), 74-95.
Mathematical Reviews (MathSciNet): MR2054533
Zentralblatt MATH: 1057.46007
Digital Object Identifier: doi:10.1002/mana.200310160
S.G. Krein, Ju.I. Petunin and E.M. Semenov, Interpolation of linear operators, AMS Transl. Math. Monographs 54, 1982.
Mathematical Reviews (MathSciNet): MR649411
G. Lewicki and G. Trombetta, Optimal and one-complemented subspaces, Monatsh. Math. 153 (2008), 115-132.
Mathematical Reviews (MathSciNet): MR2373365
J. Lindenstrauss, On projections with norm $1$-An example, Proc. Amer. Math. Soc. 15 (1964), 403-406.
Mathematical Reviews (MathSciNet): MR161126
Zentralblatt MATH: 0125.06601
Digital Object Identifier: doi:10.2307/2034513
J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Springer-Verlag, New York, 1977.
Mathematical Reviews (MathSciNet): MR500056
Zentralblatt MATH: 0362.46013
--------, Classical Banach spaces II, Springer-Verlag, New York, 1979.
Mathematical Reviews (MathSciNet): MR540367
Zentralblatt MATH: 0403.46022
A. Moltó, V. Montesinos and S. Troyanski, On quasi-denting points, denting faces and the geometry of the unit ball of $d(w,1)$, Arch. Math. 63 (1994), 45-55.
B. Randrianantoanina, Norm one projections in Banach spaces, Taiwanese J. Math. 5 (2001), 35-95.
Mathematical Reviews (MathSciNet): MR1816130
Zentralblatt MATH: 0997.46017
Y. Raynaud, On Lorentz-Sharpley spaces, Interpolation spaces and related topics (Haifa, 1990), 207-228, Israel Math. Conf. Proc. 5, Bar-Ilan University, Ramat Gan, 1992.
Mathematical Reviews (MathSciNet): MR1206503
Zentralblatt MATH: 0864.46013
U. Westphal, Cosuns in $l^p(n)$, J. Approx. Theory 54 (1988), 287-305.
Mathematical Reviews (MathSciNet): MR960051
Zentralblatt MATH: 0658.41012
Digital Object Identifier: doi:10.1016/0021-9045(88)90005-6

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Rocky Mountain Journal of Mathematics

Rocky Mountain Journal of Mathematics