Uniform non l -ness of l∞-sums of Banach spaces

• Autorzy: Kato M. , Tamura T.
• Języki publikacji: EN

Abstrakty

EN

We shall characterize the uniform non-l {...} -ness of `l∞-sums of Banach spaces (X1 ⊕ź ź ź⊕Xm)1. As applications, some results on super-reflexivity and the fixed point property for nonexpansive mappings will be presented.

Słowa kluczowe

EN

l-sum of Banach spaces; uniformly non-square space; super-reflexivity; fixed-point property; constant R(a,X)

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2009
• Tom: Vol. 49, [Z] 2
• Strony: 179--187
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Kato M.

autor

Tamura T.

• Department of Basic Sciences, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan,

Bibliografia

• [1] J.M. Ayerbe Toredano, T. T. Dom´ınguez Benavides and G. López Acedo, Measure of noncompactness in metric fixed point theory, Birkha¨uzer, 1997.
• [2] B. Beauzamy, Introduction to Banach Spaces and their Geometry, 2nd ed., North-Holland, 1985.
• [3] D. R. Brown, B-convexity in Banach spaces, Doctoral dissertation, Ohio State University, 1970.
• [4] Y. Cui, H. Hudzik and Y. Li, On the Garc´ıa-Falset coefficient in some Banach sequence spaces, Function Spaces and Applications, Lecture Notes in Pure and Appl. Math. 213 (2000), 141-148.
• [5] M. Denker and H. Hudzik, Uniformly non-l(1) n Musielak-Orlicz sequence spaces, Proc. Indian Acad. Sci. Math. Sci. 101(1991), 71-86.
• [6] T. Domınguez Benavides, Some properties of the set and ball measures of noncompactness and applications, J. London Math. Soc. 34 (1986), 120-128.
• [7] T. Domınguez Benavides, A geometrical coefficient implying the fixed point property and stability results, Houston J. Math. 22 (1996), 835-849.
• [8] J. Garcıa-Falset, Stability and fixed points for nonexpansive mappings, Houston J. Math. 20 (1994), 495-506.
• [9] J. Garcıa-Falset, E. Llorens-Fuster and Eva M. Mazcunan-Navarro, Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings, J. Funct. Anal. 233 (2006), 494-514.
• [10] D. P. Giesy, On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc. 125 (1966), 114-146.
• [11] R. Grząślewicz, H. Hudzik and W. Orlicz. Uniformly non-l (1) n property in some Orlicz spaces, Bull. Acad. Polon. Sci. Math. 34(3-4) (1986), 161-171.
• [12] H. Hudzik, Uniformly non-l(1) n Orlicz spaces with Luxemburg norm, Studia Math. 81 (1985), 271-284.
• [13] H. Hudzik, A. Kaminska and W. Kurc, Uniformly non-l(1) n Musielak-Orlicz spaces, Bull. Acad. Polon. Sci. Math. 35 (1987), 441-448.
• [14] C. James, Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542-550.
• [15] C. James, Super-reflexive Banach spaces, Canad. J. Math. 24 (1972), 896-904.
• [16] C. James, A nonreflexive Banach space that is uniformly nonoctahedral, Israel J. Math. 18 (1974), 145-155.
• [17] M. Kato, K.-S. Saito and T. Tamura, Uniform non-squareness of -direct sums of Banach spaces X _ Y , Math. Inequal. Appl. 7 (2004), 429-437.
• [18] M. Kato, K.-S. Saito and T. Tamura, Sharp triangle inequality and its reverse in Banach spaces, Math. Inequal. Appl. 10 (2007), 451-460.
• [19] M. Kato, K.-S. Saito and T. Tamura, Uniform non-`n1 -ness of -direct sums of Banach spaces X _ Y , to appear in J. Nonlinear Convex Anal.
• [20] M. Kato and T. Tamura, Uniform non-`n1 -ness of `1-sums of Banach spaces, Comment. Math. Prace Mat. 47 (2007), 161-169.