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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.
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.
3.
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.
4.
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 .
5.
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 .
6.
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 .
7.
Jin-Hong Kim 《Proceedings of the American Mathematical Society》2000,128(3):865-871
In this article we show that when the structure group of the reducible principal bundle is and is an -subbundle of , the rank of the holonomy group of a connection which is gauge equivalent to its conjugate connection is less than or equal to , and use the estimate to show that for all odd prime , if the holonomy group of the irreducible connection as above is simple and is not isomorphic to , , or , then it is isomorphic to .
8.
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 , .
9.
Antonios Broumas 《Proceedings of the American Mathematical Society》2000,128(3):677-681
Let be the Tate curve with canonical differential, . If the characteristic is , then the Hasse invariant, , of the pair should equal one. If , then calculation of leads to a nontrivial separable relation between the coefficients and . If or , Thakur related and via elementary methods and an identity of Ramanujan. Here, we treat uniformly all characteristics via explicit calculation of the formal group law of . Our analysis was motivated by the study of the invariant which is an infinite Witt vector generalizing the Hasse invariant.
10.
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 ).
11.
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 .
12.
Lá szló Zsidó 《Proceedings of the American Mathematical Society》2000,128(7):2001-2006
The goal of the paper is to prove the following theorem: if , are unital -algebras, simple and nuclear, then any -subalgebra of the -tensor product of and , which contains the tensor product of with the scalar multiples of the unit of , splits in the -tensor product of with some -subalgebra of .
13.
Ralf Kemper 《Proceedings of the American Mathematical Society》2000,128(3):709-712
It is an open question as to whether every left coherent ring satisfying the intersection property for finitely generated left ideals of is a right-product-trace-ring or not. is a right-product-trace-ring iff every product of trace-right--modules (= universally torsionless-right--modules) is a trace-right--module. This question is shown to have a negative answer. Furthermore, looking at all valuation domains, the complete product-trace-rings, the product-trace-rings and the product-content-rings are characterized.
14.
Cristian D. Gonzalez-Avilé s 《Proceedings of the American Mathematical Society》2000,128(4):953-961
Let be a finite Galois extension of number fields with Galois group , let be an abelian variety defined over , and let and denote, respectively, the Tate-Shafarevich groups of over and of over . Assuming that these groups are finite, we derive, under certain restrictions on and , a formula for the order of the subgroup of of -invariant elements. As a corollary, we obtain a simple formula relating the orders of , and when is a quadratic extension and is the twist of by the non-trivial character of .
15.
Tomoaki Ono 《Proceedings of the American Mathematical Society》2000,128(2):353-360
Let be a tower of rings of characteristic . Suppose that is a finitely presented -module. We give necessary and sufficient conditions for the existence of -bases of over . Next, let be a polynomial ring where is a perfect field of characteristic , and let be a regular noetherian subring of containing such that . Suppose that is a free -module. Then, applying the above result to a tower of rings, we shall show that a polynomial of minimal degree in is a -basis of over .
16.
Let be a non-trivial finite Galois extension of a field . In this paper we investigate the role that valuation-theoretic properties of play in determining the non-triviality of the relative Brauer group, , of over . In particular, we show that when is finitely generated of transcendence degree 1 over a -adic field and is a prime dividing , then the following conditions are equivalent: (i) the -primary component, , is non-trivial, (ii) is infinite, and (iii) there exists a valuation of trivial on such that divides the order of the decomposition group of at .
17.
M. E. Rossi 《Proceedings of the American Mathematical Society》2000,128(5):1325-1332
Let be a local ring of positive dimension and let be an -primary ideal. We denote the reduction number of by , which is the smallest integer such that for some reduction of In this paper we give an upper bound on in terms of numerical invariants which are related with the Hilbert coefficients of when is Cohen-Macaulay. If , it is known that where denotes the multiplicity of If in Corollary 1.5 we prove where is the first Hilbert coefficient of From this bound several results follow. Theorem 1.3 gives an upper bound on in a more general setting.
18.
Francisco F. Lasheras 《Proceedings of the American Mathematical Society》2000,128(3):893-902
In this paper we give a characterization of those locally finite -dimensional simplicial complexes that have an orientable -manifold thickening. This leads to an obstruction for a fake surface to admit such a thickening. The obstruction is defined in , where is the subgraph consisting of all the -simplexes of order three.
19.
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 .
20.
Senchun Lin 《Proceedings of the American Mathematical Society》2000,128(5):1459-1466
Suppose that and are Minkowski Gauss curvature and Minkowski mean curvature respectively on a timelike surface that is immersed in Minkowski 3-space . Suppose also that and that is complete as a surface in the underlying Euclidean 3-space . It is shown that neither nor can be bounded away from zero on such a surface .