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Advanced Courses of Mathematical Analysis I: Proceedings of by A. Aizpuru-Tomas, F. Leon-Saavedra

By A. Aizpuru-Tomas, F. Leon-Saavedra

This quantity includes a suite of articles from specialists with a wealthy study and academic adventure. The members of this quantity are: Y Benyamini, M Gonzбlez, V Mьller, S Reich, E Matouskova, A J Zaslavski and A R Palacios. each one in their paintings is beneficial. for instance, Benyamini's is the one up-to-date survey of the intriguing and lively zone of the type of Banach areas lower than uniformly non-stop maps whereas Gonzбlez's article is a pioneer advent to the speculation of neighborhood duality for Banach areas.

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Séminaire Bourbaki, Vol. 43, 2000-2001, Exp. 880-893

Desk of Contents

Seminaire Bourbaki quantity forty three web page 1 2000-2001 [doi UNKNOWN] Laurent Bonavero -- Factorisation faible des functions birationnelles

Seminaire Bourbaki quantity forty three web page 39 2000-2001 [doi UNKNOWN] Marco Brunella -- Courbes entieres dans les surfaces algebriques complexes

Seminaire Bourbaki quantity forty three web page sixty three 2000-2001 [doi UNKNOWN] Michel Emery -- Espaces probabilises filtres : de los angeles theorie de Vershik au mouvement brownien, through des idees de Tsirelson

Seminaire Bourbaki quantity forty three web page eighty five 2000-2001 [doi UNKNOWN] Marc Herzlich -- Linegalite de Penrose

Seminaire Bourbaki quantity forty three web page 113 2000-2001 [doi UNKNOWN] Michele Audin -- Integrabilite et non-integrabilite de systemes hamiltoniens

Seminaire Bourbaki quantity forty three web page 137 2000-2001 [doi UNKNOWN] Pierre Cartier -- Fonctions polylogarithmes, nombres polyzetas et groupes pro-unipotents

Seminaire Bourbaki quantity forty three web page one hundred seventy five 2000-2001 [doi UNKNOWN] Antoine Chambert-Loir -- Theoremes d algebricite en geometrie diophantienne

Seminaire Bourbaki quantity forty three web page 211 2000-2001 [doi UNKNOWN] Philippe Michel -- Repartition des zeros des fonctions L et matrices aleatoires

Seminaire Bourbaki quantity forty three web page 249 2000-2001 [doi UNKNOWN] Michele Vergne -- Quantification geometrique et aid symplectique

Seminaire Bourbaki quantity forty three web page 279 2000-2001 [doi UNKNOWN] Philippe Biane -- Entropie libre et algebres d operateurs

Seminaire Bourbaki quantity forty three web page 301 2000-2001 [doi UNKNOWN] man Henniart -- Progres recents en fonctorialite de Langlands

Seminaire Bourbaki quantity forty three web page 323 2000-2001 [doi UNKNOWN] Emmanuel Peyre -- issues de hauteur bornee et geometrie des varietes

Seminaire Bourbaki quantity forty three web page 345 2000-2001 [doi UNKNOWN] Georges Skandalis -- Geometrie non commutative, operateur de signature transverse et algebres de Hopf

Seminaire Bourbaki quantity forty three web page 365 2000-2001 [doi UNKNOWN] Cedric Villani -- Limites hydrodynamiques de l equation de Boltzmann

Extra info for Advanced Courses of Mathematical Analysis I: Proceedings of the First International School

Example text

A more precise statement is given by the following theorem. Recall that a subset M c X is called residual if its complement X \ M is of the first category. Equivalently, M is residual if and only if it contains a dense G6 subset. 2. Let T E B ( X ) and let (a,) be a sequence of positive numa, = 0 . Then the set of all points x E X with the bers such that property that llTnxll 2 a,llTnll f o r infinitely many n is residual. Proof. The statement is trivial if T is nilpotent. In the following we assume that T n # 0 for all n.

We refer to l 1 for more details. It is not difficult to show that this subspace 2 is isometric to the space C(A) of the continuous functions on the Cantor set A in [0,1]. P. , a sequence of finite rank operators T, acting on X so that lim IIT,a: - a:((= 0 for all 5 E X , n+m 44 (b) lim llTnll = 1 and n-co ( c ) TnTk = TkTn = Tmin{k,n); Using this fact we can prove the following result. , and let (T,) be a commuting 1-approximating sequence o n X . P. Theorem 12. 15 in Remark 13. Let X be a space with a monotone basis.

CLAIM:There exists an integer n such that Pn satisfies the properties of the map L associated to F , G and E in Theorem 3. Indeed, taking into account that the unit ball of a finite dimensional space is compact, (a) follows from (l),(b’) follows from (2) and (c’) follows from (3). Although the definition of local dual space is “local”, we shall see in Theorem 5 that it is possible to give “global” characterizations. The following result will be useful. Proposition 4. Let 2 be a local dual of X .

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