Uniform non-ln1-ness of l_1-sums of Banach spaces

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

Abstrakty

EN

We shall characterize the uniform non-`n1-ness of the `1-sum (X1 +ź ź ź + X_m)_1 of a finite number of Banach spaces X_1, ź ź ź ,X_m. Also we shall obtain that (X_1 +ź ź ź +X_m)_1 is uniformly non-lm+1 if and only if all X_1, . . . ,X_m are uniformly non-square (note that (X_1 + ź ź ź +X_m)_1 is not uniformly non-lm1). Several related results will be presented.

Słowa kluczowe

EN

l_1-sum of Banach spaces; uniformly non-square space; uniformly non-l_n1 space; super-reflexivity; fixed-point property

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2007
• Tom: Vol. 47, [Z] 2
• Strony: 161--169
• Opis fizyczny: bibliogr. 17 poz.

Twórcy

autor

Kato M.

autor

Tamura T.

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

Bibliografia

• [1] G. Alherk and H. Hudzik, Uniformly non-l(1) n Musielak-Orlicz spaces of Bochner type, Forum Math 1 (1989), 403-410.
• [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, Ohaio State University 1970.
• [4] M. Denker and H. Hudzik, Uniformly non-l(1)n Musielak-Orlicz sequence spaces, Proc. Indian Acad. Sci. Math. Sci. 101 (1991), 71-86.
• [5] D.P. Giesy, On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc. 125 (1966), 114-146.
• [6] J. Garcia-Falset, E. Llorens-Fuster and E.M. Mazcunan-Navarro, Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings, J. Funct. Anal. 233 (2006), 494-514.
• [7] 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.
• [8] H. Hudzik, Uniformly non-l(1)n Orlicz spaces with Luxemburg norm, Studia Math. 81 (1985), 271-284.
• [9] H. Hudzik, A. Kamińska and W. Kurc, Uniformly non-l(1) n Musielak-Orlicz spaces, Bull. Acad. Polon. Sci. Math. 35 (1987), 7-8.
• [10] C. James, Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542-550.
• [11] C. James, Super-reflexive Banach spaces, Canad. J. Math. 24 (1972), 896-904.
• [12] C. James, A nonreflexive Banach space that is uniformly nonoctahedral, Israel J. Math. 18 (1974), 145-155.
• [13] M. Kato, K.-S. Saito and T. Tamura, Uniform non-squareness of ψdirect sums of Banach spaces X _ψ Y , Math. Inequal. Appl. 7 (2004), 429-437.
• [14] M. Kato, K.-S. Saito and T. Tamura, Sharp triangle inequality and its reverse in Banach spaces, Math. Inequal. Appl. 10 (2007), 451-460.
• [15] M. Kato, K.-S. Saito and T. Tamura, Uniform non-n1 -ness of -direct sums of Banach spaces X _ ψY , submitted.
• [16] R.E. Megginson, An Introduction to Banach Space Theory, Springer Verlag 1998.
• [17] K.-I. Mitani, K.-S. Saito, M. Kato and T. Tamura, On sharp triangle inequalities in Banach spaces, J. Math. Anal. Appl. 336 (2007), 1178-1186.