Banach Space Theory and its Applications: Proceedings of the by Jonathan Arazy (auth.), Albrecht Pietsch, Nicolae Popa, Ivan

By Jonathan Arazy (auth.), Albrecht Pietsch, Nicolae Popa, Ivan Singer (eds.)

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Additional info for Banach Space Theory and its Applications: Proceedings of the First Romanian-GDR Seminar Held at Bucharest, Romania, August 31 – September 6, 1981

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V of X' w i t h to V'. the e x i s t e n c e with respect space. such that X has p r o p e r t y 2) is s a t i s f i e d isomorphic l) i m p l i e s V of X' w i t h p o s i t i v e sequentially condition Banach linear subspace characteristic In a d d i t i o n , Proof: to a c o n j u g a t e a closed to o(X,V). implies Therefore to that X is of I. S i n g e r [14~. we get the f o l l o w i n g isometric B a n a c h s p a c e X, the f o l l o w i n g version: conditions are e q u i v a l e n t : I) X is i s o m e t r i c 2) T h e r e e x i s t s char(V)=l In addition, canonically to a c o n j u g a t e a closed linear Banach such that X has p r o p e r t y condition isometric 2) is s a t i s f i e d to V'.

4. : On the center of a convex set, Dokl. Akad. ), 59(1948), 837-840. Equivalent norms and the fixed point property for nonexpansive mappings. J. London Math. Soc. , 10(4) 5. : (1982), 139-144. Banach spaces which are nearly uniformly convex, Rocky Mountain Jour(1980), 743-749. A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly, 72(1965), 1004-1006. 6. : Asymptotic centers and nonexpansive mappings in conjugate Banach spaces, Pac. J. Math. 90(1980), 135-143.

The linear (,) in E of G is equivalent property subspace of G, called by G of E is called with 51 1 i~ - ball property in E, if the conditions gaG, x~E, ri~0 , i=1,2 G~BE(X,r2)#0 and I Ix-gl I

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