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1.
Fangyan Lu 《Proceedings of the American Mathematical Society》2003,131(12):3883-3892
Let be a subalgebra of a nest algebra . If contains all rank one operators in , then is said to be large; if the set of rank one operators in coincides with that in the Jacobson radical of , is said to be radical-type. In this paper, algebraic isomorphisms of large subalgebras and of radical-type subalgebras are characterized. Let be a nest of subspaces of a Hilbert space and be a subalgebra of the nest algebra associated to (). Let be an algebraic isomorphism from onto . It is proved that is spatial if one of the following occurs: (1) () is large and contains a masa; (2) () is large and closed; (3) () is a closed radical-type subalgebra and ( is quasi-continuous (i.e. the trivial elements of are limit points); (4) () is large and one of and is not quasi-continuous.
2.
Donatella Danielli Nicola Garofalo Duy-Minh Nhieu 《Proceedings of the American Mathematical Society》2003,131(11):3487-3498
Let be a group of Heisenberg type with homogeneous dimension . For every we construct a non-divergence form operator and a non-trivial solution to the Dirichlet problem: in , on . This non-uniqueness result shows the impossibility of controlling the maximum of with an norm of when . Another consequence is the impossiblity of an Alexandrov-Bakelman type estimate such as
where is the dimension of the horizontal layer of the Lie algebra and is the symmetrized horizontal Hessian of .
where is the dimension of the horizontal layer of the Lie algebra and is the symmetrized horizontal Hessian of .
3.
Masaharu Kusuda 《Proceedings of the American Mathematical Society》2003,131(10):3075-3081
Let be a -algebra and let be a full (right) Hilbert -module. It is shown that if the spectrum of is discrete, then every closed --submodule of is complemented in , and conversely that if is a -space and if every closed --submodule of is complemented in , then is discrete.
4.
Sergey S. Goncharov Valentina S. Harizanov Michael C. Laskowski Steffen Lempp Charles F. D. McCoy 《Proceedings of the American Mathematical Society》2003,131(12):3901-3912
We prove that if is any model of a trivial, strongly minimal theory, then the elementary diagram is a model complete -theory. We conclude that all countable models of a trivial, strongly minimal theory with at least one computable model are -decidable, and that the spectrum of computable models of any trivial, strongly minimal theory is .
5.
Edward L. Green Nicole Snashall Ø yvind Solberg 《Proceedings of the American Mathematical Society》2003,131(11):3387-3393
This paper describes the Hochschild cohomology ring of a selfinjective algebra of finite representation type over an algebraically closed field , showing that the quotient of the Hochschild cohomology ring by the ideal generated by all homogeneous nilpotent elements is isomorphic to either or , and is thus finitely generated as an algebra. We also consider more generally the property of a finite dimensional algebra being selfinjective, and as a consequence show that if all simple -modules are -periodic, then is selfinjective.
6.
Matej Bresar Ajda Fosner Peter Semrl 《Proceedings of the American Mathematical Society》2003,131(12):3833-3837
Let be be semisimple Banach algebras and let be a unital bijective linear operator that preserves invertibility. If the socle of is an essential ideal of , then is a Jordan isomorphism.
7.
Etienne Desquith 《Proceedings of the American Mathematical Society》2003,131(7):2109-2119
Given a Banach algebra , R. Larsen defined, in his book ``An introduction to the theory of multipliers", a Banach algebra by means of a multiplier on , and essentially used it in the case of a commutative semisimple Banach algebra to prove a result on multiplications which preserve regular maximal ideals. Here, we consider the analogue Banach algebra induced by a bounded double centralizer of a Banach algebra . Then, our main concern is devoted to the relationships between , , and the algebras of bounded double centralizers and of and , respectively. By removing the assumption of semisimplicity, we generalize some results proven by Larsen.
8.
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 .
9.
Yifeng Xue 《Proceedings of the American Mathematical Society》2007,135(3):705-711
A unital -algebra is said to have the (APD)-property if every nonzero element in has the approximate polar decomposition. Let be a closed ideal of . Suppose that and have (APD). In this paper, we give a necessary and sufficient condition that makes have (APD). Furthermore, we show that if and or is a simple purely infinite -algebra, then has (APD).
10.
N. Mohan Kumar Chris Peterson A. Prabhakar Rao 《Proceedings of the American Mathematical Society》2003,131(12):3681-3688
We construct families of rank two bundles on , in characteristic two, where for , is a sum of line bundles, and is non-split. We construct families of rank two bundles on , in characteristic , where for , is a sum of line bundles, and is non-split.
11.
Wen-Fong Ke Bing-Ren Li Ngai-Ching Wong 《Proceedings of the American Mathematical Society》2004,132(7):1979-1985
Let be locally compact Hausdorff spaces and , be Banach algebras. Let be a zero product preserving bounded linear map with dense range. We show that is given by a continuous field of algebra homomorphisms from into if is irreducible. As corollaries, such a surjective arises from an algebra homomorphism, provided that is a -algebra and is a semi-simple Banach algebra, or both and are -algebras.
12.
Rü diger Gö bel Warren May 《Proceedings of the American Mathematical Society》2003,131(10):2987-2992
Under the assumptions of MA and CH, it is proved that if is a field of prime characteristic and is an -separable abelian -group of cardinality , then an isomorphism of the group algebras and implies an isomorphism of and .
13.
Robert Gilmer 《Proceedings of the American Mathematical Society》2003,131(8):2337-2346
Let be an integral domain with quotient field and integral closure . An overring of is a subring of containing , and denotes the set of overrings of . We consider primarily two finiteness conditions on : (FO), which states that is finite, and (FC), the condition that each chain of distinct elements of is finite. (FO) is strictly stronger than (FC), but if , each of (FO) and (FC) is equivalent to the condition that is a Prüfer domain with finite prime spectrum. In general satisfies (FC) iff satisfies (FC) and all chains of subrings of containing have finite length. The corresponding statement for (FO) is also valid.
14.
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.
15.
Nobuhiro Asai Izumi Kubo Hui-Hsiung Kuo 《Proceedings of the American Mathematical Society》2003,131(3):815-823
Let and denote the Gaussian and Poisson measures on , respectively. We show that there exists a unique measure on such that under the Segal-Bargmann transform the space is isomorphic to the space of analytic -functions on with respect to . We also introduce the Segal-Bargmann transform for the Poisson measure and prove the corresponding result. As a consequence, when and have the same variance, and are isomorphic to the same space under the - and -transforms, respectively. However, we show that the multiplication operators by on and on act quite differently on .
16.
Stephen J. Gardiner Mary Hanley 《Proceedings of the American Mathematical Society》2003,131(3):773-779
Let denote a relatively closed subset of the unit ball of . The purpose of this paper is to characterize those sets which have the following property: any harmonic function on which satisfies on (where 0$">) can be locally uniformly approximated on by a sequence of harmonic polynomials which satisfy the same inequality on . This answers a question posed by Stray, who had earlier solved the corresponding problem for holomorphic functions on the unit disc.
17.
Erik Jensen 《Proceedings of the American Mathematical Society》2008,136(1):181-192
Let denote the measure-preserving Hénon map with the parameter . The map has a hyperbolic fixed point . The main result of this paper is that the unstable mainfold of is the iterated limit of a very simple set. Informally, where is the line and denotes the unstable manifold of .
18.
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 ().
19.
E. Serrano C. Piñ eiro J. M. Delgado 《Proceedings of the American Mathematical Society》2006,134(3):689-695
Let and be Banach spaces. We say that a set denotes the space of all compact operators from into ) is equicompact if there exists a null sequence in such that for all and all . It is easy to show that collectively compactness and equicompactness are dual concepts in the following sense: is equicompact iff is collectively compact. We study some properties of equicompact sets and, among other results, we prove: 1) a set is equicompact iff each bounded sequence in has a subsequence such that is a converging sequence uniformly for ; 2) if does not have finite cotype and is a maximal equicompact set, then, given and a finite set in , there is an operator such that for and all .
20.
I. Gasparis 《Proceedings of the American Mathematical Society》2001,129(3):759-764
The following dichotomy is established for any pair , of hereditary families of finite subsets of : Given , an infinite subset of , there exists an infinite subset of so that either , or , where denotes the set of all finite subsets of .