共查询到20条相似文献,搜索用时 46 毫秒
1.
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.
2.
Fabio Nicola 《Proceedings of the American Mathematical Society》2003,131(9):2841-2848
We are concerned with the so-called -pseudo-differential calculus. We describe the spectrum of the unital and commutative -algebra given by the norm closure of the space of -order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their -theory is computed.
3.
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 .
4.
Ljiljana Arambasic 《Proceedings of the American Mathematical Society》2007,135(2):469-478
Let be a countably generated Hilbert -module over a -algebra We prove that a sequence is a standard frame for if and only if the sum converges in norm for every and if there are constants such that for every We also prove that surjective adjointable operators preserve standard frames. A class of frames for countably generated Hilbert -modules over the -algebra of all compact operators on some Hilbert space is discussed.
5.
Florian Enescu 《Proceedings of the American Mathematical Society》2003,131(11):3379-3386
The notion of stability of the highest local cohomology module with respect to the Frobenius functor originates in the work of R. Hartshorne and R. Speiser. R. Fedder and K.-i. Watanabe examined this concept for isolated singularities by relating it to -rationality. The purpose of this note is to study what happens in the case of non-isolated singularities and to show how this stability concept encapsulates a few of the subtleties of tight closure theory. Our study can be seen as a generalization of the work by Fedder and Watanabe. We introduce two new ring invariants, the -stability number and the set of -stable primes. We associate to every ideal generated by a system of parameters and an ideal of multipliers denoted and obtain a family of ideals . The set is independent of and consists of finitely many prime ideals. It also equals prime ideal such that is -stable. The maximal height of such primes defines the -stability number.
6.
Gabriel Navarro 《Proceedings of the American Mathematical Society》2003,131(10):3019-3020
If is a finite group and is a prime number, let be the number of Sylow -subgroups of . If is a subgroup of a -solvable group , we prove that divides .
7.
Michael J. Fisher 《Proceedings of the American Mathematical Society》2003,131(11):3617-3621
Let be a fixed odd prime. In this paper we prove an exponent conjecture of Bousfield, namely that the -exponent of the spectrum is for . It follows from this result that the -exponent of is at least for and , where denotes the -connected cover of .
8.
Damir Bakic 《Proceedings of the American Mathematical Society》2005,133(2):441-448
We prove the following generalization of the noncommutative Tietze extension theorem: if is a countably generated Hilbert -module over a -unital -algebra, then the canonical extension of a surjective morphism of Hilbert -modules to extended (multiplier) modules, , is also surjective.
9.
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 .
10.
Lin Chen Ruan Yingbin Yan Zikun 《Proceedings of the American Mathematical Society》2003,131(9):2753-2759
We prove that if are injective, then is subscalar if and only if is subscalar. As corollaries, it is shown that -hyponormal operators and log-hyponormal operators are subscalar; also w-hyponormal operators with Ker Kerand their generalized Aluthge transformations are subscalar.
11.
Madjid Mirzavaziri Mohammad Sal Moslehian 《Proceedings of the American Mathematical Society》2006,134(11):3319-3327
Let be a -algebra acting on a Hilbert space , let be a linear mapping and let be a -derivation. Generalizing the celebrated theorem of Sakai, we prove that if is a continuous -mapping, then is automatically continuous. In addition, we show the converse is true in the sense that if is a continuous --derivation, then there exists a continuous linear mapping such that is a --derivation. The continuity of the so-called - -derivations is also discussed.
12.
Let be a rational prime and a positive rational integer coprime with . Denote by the number of solutions of the equation in rational integers and . In a paper of Le, he claimed that without giving a proof. Furthermore, the statement has been used by Le, Bugeaud and Shorey in their papers to derive results on certain Diophantine equations. In this paper we point out that the statement is incorrect by proving that .
13.
Rü diger Gö bel Warren May 《Proceedings of the American Mathematical Society》2003,131(9):2705-2710
Let be abelian groups where is a direct sum of countable -groups. A condition is given on the Ulm-Kaplansky -invariants of and such that .
14.
Fernando Szechtman 《Proceedings of the American Mathematical Society》2003,131(12):3657-3664
We refer to an automorphism of a group as -inner if given any subset of with cardinality less than , there exists an inner automorphism of agreeing with on . Hence is 2-inner if it sends every element of to a conjugate. New examples are given of outer -inner automorphisms of finite groups for all natural numbers .
15.
Martin Mathieu 《Proceedings of the American Mathematical Society》2004,132(2):443-446
A linear mapping from a subspace of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant such that for all , where denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple -algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.
16.
Stephen Allen David Pask Aidan Sims 《Proceedings of the American Mathematical Society》2006,134(2):455-464
Given a -graph and an element of , we define the dual -graph, . We show that when is row-finite and has no sources, the -algebras and coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the -theory of when is finite and strongly connected and satisfies the aperiodicity condition.
17.
18.
We study the complexification of real Hilbert -modules over real -algebras. We give an example of a Hilbert -module that is not the complexification of any Hilbert -module, where is a real -algebra.
19.
Huaxin Lin 《Proceedings of the American Mathematical Society》2004,132(11):3215-3224
Let be a non-unital and -unital simple -algebra. We show that if is simple, then is purely infinite. We also show that is simple if and only if has a continuous scale provided that is not isomorphic to the compact operators.
20.
N. Bejhaj Rhouma 《Proceedings of the American Mathematical Society》2003,131(12):3747-3755
We show the existence of principal eigenvalues of the problem in where is an indefinite weight function. The existence of a continuous family of principal eigenvalues is demonstrated. Also, we prove the existence of a principal eigenvalue for which the principal eigenfunction at .