By G. Coeuré (Eds.)
Coeure G. Analytic capabilities and manifolds in endless dimensional areas (NHMS, NH, 1974)(ISBN 0444106219)
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Additional resources for Analytic Functions and Manifolds in Infinite Dimensional Spaces
F. map F + f. u = TI P . P By t h e first s t e p , t h e r e e x i s t s ..
Proof. - B r i s normed, t h e r e e x i s t s p a c e s corollary. Actually, we take f o r X El B , we is metrizable i f f E' a When i s a Frechet space. Eb space t h e n E have E - B ;El i s normable ' with properties of t h e r a s p a c e of t y p e , such t h a t p(w) AU , with u a n admis- i s bounded, a l l w E , A g e n e r a l t y p e o f s t r o n g l y - i n v a r i a n t by d e r i v a t i o n s p a c e s . i f , for any w E such that w A coveringg of e + u V by open s e t s w i l l be called admissible X there e x i s t s V balanced neighbourhood of t h e o r i g i n i n is contained i n some ~ ' 6 u .
B) t h e proof i s complete. - The theorem 6 . 1 6 i s proved m. Aurich [S] f o r t h e b-topology by a more d i f f i c u l t way t h a n h e r e . C. Matos. - Vector v a l u e d e x t e n s i o n s . L e t a complex s e q u e n t i a l l y complete c . v . s . E s p r e a d o v e r a n o t h e r complex c . v . s . - . OE(W for P r o o f . - Given f be g i v e n . - a s a n e x t e n s i o n of Suppose [17,48,80]. for . The mapping (6y(Y,F) . For i s contained i n v a n i s h e s and t h e r e f o r e t h e r a n g e o f thus, is an e x t e n s i o n Every OX(X,F)-extension Y f o r W E ( F ) 6 x ( ~ ,and ~ )h a s belongs t o 5 f and a m a n i f o l d (X,p) F 0 y(Y,6?
Analytic Functions and Manifolds in Infinite Dimensional Spaces by G. Coeuré (Eds.)