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1.
A generalization of Kwack's theorem to the infinite dimensional case is obtained. We consider a holomorphic map from into , where is a hypersurface in a complex Banach manifold and is a hyperbolic Banach space. Under various assumptions on , and we show that can be extended to a holomorphic map from into . Moreover, it is proved that an increasing union of pseudoconvex domains containing no complex lines has the Hartogs extension property.
2.
Byeong-Kweon Oh 《Proceedings of the American Mathematical Society》2000,128(3):683-689
Let be the minimal rank of -universal -lattices, by which we mean positive definite -lattices which represent all positive -lattices of rank . It is a well known fact that for . In this paper, we determine and find all -universal lattices of rank for .
3.
Let be an integer and let be a domain of . Let be an injective mapping which takes hyperspheres whose interior is contained in to hyperspheres in . Then is the restriction of a Möbius transformation.
4.
Ignacio Villanueva 《Proceedings of the American Mathematical Society》2000,128(3):793-801
Given a -linear operator from a product of spaces into a Banach space , our main result proves the equivalence between being completely continuous, having an -valued separately continuous extension to the product of the biduals and having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to being weakly compact, and that, for , being weakly compact implies the conditions above but the converse fails.
5.
Simeon T. Stefanov 《Proceedings of the American Mathematical Society》2000,128(3):885-891
For any a -dimensional polyhedron is constructed such that the Yang index of its deleted product equals . This answers a question of Izydorek and Jaworowski (1995). For any a -dimensional closed manifold with involution is constructed such that , but can be mapped into a -dimensional polyhedron without antipodal coincidence.
6.
Alexander Kleshchev Alexander Premet 《Proceedings of the American Mathematical Society》2000,128(3):647-655
Let be an algebraic number field and be the ring of integers of . Let be a finite group and be a finitely generated torsion free -module. We say that is a globally irreducible -module if, for every maximal ideal of , the -module is irreducible, where stands for the residue field .
Answering a question of Pham Huu Tiep, we prove that the symmetric group does not have non-trivial globally irreducible modules. More precisely we establish that if is a globally irreducible -module, then is an -module of rank with the trivial or sign action of .
7.
Harald K. Wimmer 《Proceedings of the American Mathematical Society》2000,128(3):873-876
Let and be complementary spaces of a finite dimensional unitary space and let denote the projection of on parallel to . Estimates for the norm of are derived which involve the norm of the restriction of to or the gap between and .
8.
Matthias Hieber Sylvie Monniaux 《Proceedings of the American Mathematical Society》2000,128(4):1047-1053
In this paper, we show that a pseudo-differential operator associated to a symbol ( being a Hilbert space) which admits a holomorphic extension to a suitable sector of acts as a bounded operator on . By showing that maximal -regularity for the non-autonomous parabolic equation is independent of , we obtain as a consequence a maximal -regularity result for solutions of the above equation.
9.
Larry Smith 《Proceedings of the American Mathematical Society》2000,128(8):2199-2201
Let be a finite group and a complex representation. Barbara Schmid has shown that the algebra of invariant polynomial functions on the vector space is generated by homogeneous polynomials of degree at most , where is the largest degree of a generator in a minimal generating set for , and is the complex regular representation of . In this note we give a new proof of this result, and at the same time extend it to fields whose characteristic is larger than , the order of the group .
10.
Alexandre Eremenko 《Proceedings of the American Mathematical Society》2000,128(2):557-560
Bloch's Theorem is extended to -quasiregular maps , where is the standard -dimensional sphere. An example shows that Bloch's constant actually depends on for .
11.
Karel Dekimpe 《Proceedings of the American Mathematical Society》2003,131(3):973-978
We are dealing with Lie groups which are diffeomorphic to , for some . After identifying with , the multiplication on can be seen as a map . We show that if is a polynomial map in one of the two (sets of) variables or , then is solvable. Moreover, if one knows that is polynomial in one of the variables, the group is nilpotent if and only if is polynomial in both its variables.
12.
Xavier Massaneda Pascal J. Thomas 《Proceedings of the American Mathematical Society》2000,128(3):837-843
We show that a sequence in the unit ball of is sampling for the Hardy spaces , , if and only if the admissible accumulation set of in the unit sphere has full measure. For the situation is quite different. While this condition is still sufficient, when (in contrast to the one dimensional situation) there exist sampling sequences for whose admissible accumulation set has measure 0. We also consider the sequence obtained by applying to each a random rotation, and give a necessary and sufficient condition on so that, with probability one, is of sampling for , .
13.
Djalil Kateb 《Proceedings of the American Mathematical Society》2000,128(3):735-743
Soient , et trois réels tels que , , et et soit une fonction appartenant à l'espace de Besov . Nous montrons que si est une fonction, de la variable réelle, nulle à l'origine, lipschitzienne et appartenant à l'espace on a alors . La preuve est essentiellement basée sur des résultats d'approximation par des fonctions splines de degré .
14.
A sequence of positive integers is called a -sequence if every integer has at most representations with all in and . A -sequence is also called a -sequence or Sidon sequence. The main result is the following
Theorem. Let be a -sequence and for an integer . Then there is a -sequence of size , where .
Corollary. Let . The interval then contains a -sequence of size , when .
15.
Robert Myers 《Proceedings of the American Mathematical Society》2000,128(5):1563-1566
This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open -manifold which is not homeomorphic to is a covering space of an -manifold and either or and is irreducible, then the group of covering translations injects into the homeotopy group of .
16.
The boundary behavior of the Bergman metric near a convex boundary point of a pseudoconvex domain is studied. It turns out that the Bergman metric at points in the direction of a fixed vector tends to infinity, when is approaching , if and only if the boundary of does not contain any analytic disc through in the direction of .
17.
Given a Banach space and an integer , the existence of an -homogeneous polynomial which is not uniformly continuous with respect to the polynomial topology on is investigated. We provide a complete characterization for some classical Banach spaces, while for others a surprising unresolved difficulty is encountered for a certain value of (depending on ).
18.
Wojciech Szymanski 《Proceedings of the American Mathematical Society》2000,128(3):789-791
We show that if are type factors with finite index (and common identity) and is the trace preserving conditional expectation, then there are no subdiagonal algebras in with respect to unless .
19.
Dejan Kolaric 《Proceedings of the American Mathematical Society》2008,136(4):1273-1284
Let be a closed polydisc or ball in , and let be a quasi-projective algebraic manifold which is Zariski locally equivalent to , or a complement of an algebraic subvariety of codimension in such a manifold. If is an integer satisfying , then every holomorphic map from a neighborhood of to with rank at every point of can be approximated uniformly on by entire maps with rank at every point of .
20.
Naoya Sumi 《Proceedings of the American Mathematical Society》1999,127(3):915-924
We show that on the 2-torus there exists a open set of regular maps such that every map belonging to is topologically mixing but is not Anosov. It was shown by Mañé that this property fails for the class of toral diffeomorphisms, but that the property does hold for the class of diffeomorphisms on the 3-torus . Recently Bonatti and Diaz proved that the second result of Mañé is also true for the class of diffeomorphisms on the -torus ().