By G. Coeuré (Eds.)

ISBN-10: 0080871224

ISBN-13: 9780080871226

ISBN-10: 0444106219

ISBN-13: 9780444106216

Coeure G. Analytic features and manifolds in countless dimensional areas (NHMS, NH, 1974)(ISBN 0444106219)

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**Additional info for Analytic Functions and Manifolds in Infinite Dimensional Spaces**

**Example text**

We obtain some information about the relationship between the topological spectrum sp. A the set of h C sp. - p)A A , ,a . The set of their weak continuation to A+E'op i. d, Frechet algebra in @ , ( X , C ) ; i s contained i n S(Al and ? ( A ) is a connected component Given A natural, 8. *A of q ? - First, we prove that the is contained in S(A) q E N(A) S. *A , i. d. *A , there exists . Actually, given a balanced neighbourhood V of 0 E E ,E > 0 such that : SPECTRUM AND MAXIMIL EXTENSIONS lh[fn(a)]l < 1 , all Then, s i n c e f {f E A Iq(f) -?

A particular case, E = CC' . Nothing i s known about sp* [ (3 ( x ) ] - [6 (XI] f o r a general c. v. s. 13 when E t h e product space , with set o f f i n i t e subsets o f map from @ I o n t o by (zi) with zi I is as a g e n e r a l s e t . We denote b y % (I) t h e I ; f o r any A of I ;( I ) , mA is the projection 4:A ; we i d e n t i f y g A with t h e subspace o f (rl defined = 0, i g I-A The u n i t d i s k o f d: i s w r i t t e n A . Theorem 6 . 1 4 . - Let f X , p ) be a m n i f o l d spread over d; I and suppose the mdmt extension of bfX1 i s X Then there e d 8 t s A o 6 T f I ) and a Stein mznifold i 8pread over Ao such that X is isomorphic w i t h i x &-A0 .

Let r be a s e t i n ~,(x,z); t h e s e t T f o r r i s defined by : 3 r i = { X E x [ [ [ f ( z ~ lll lf l ~ l , aZZ T-huZZ o f a bounding f cr 1 . Let 'l be a e. i. d, natura2 Frechet space i n 6xt~,~). Then T i n the I'-maximaZ extension ? - wry bounding s e t F a ) For eome neighbourhood for F , contained i n li. , V of 0 E , T + V i s a bounding s e t b ) For any balanced, open, neighbourhood V of O G E , we get : [i'fr)] 3 eup { r > 0 I T + r A a i s n bounding s e t contained i n ? all a E V 1 , Here, d i o t h e u n i t disk i n d: , V di .

### Analytic Functions and Manifolds in Infinite Dimensional Spaces by G. Coeuré (Eds.)

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