共查询到10条相似文献,搜索用时 93 毫秒
1.
Jerzy Kakol Stephen A. Saxon Aaron R. Todd 《Proceedings of the American Mathematical Society》2004,132(6):1703-1712
Let be a completely regular Hausdorff space, and let be the space of continuous real-valued functions on endowed with the compact-open topology. We find various equivalent conditions for to be a -space, resolving an old question of Jarchow and consolidating work by Jarchow, Mazon, McCoy and Todd. Included are analytic characterizations of pseudocompactness and an example that shows that, for , Grothendieck's -spaces do not coincide with Jarchow's -spaces. Any such example necessarily answers a thirty-year-old question on weak barrelledness properties for , our original motivation.
2.
Alexandre Turull 《Proceedings of the American Mathematical Society》2004,132(9):2563-2565
We observe a simple formula to compute the number of Hall -subgroups of a -separable finite group in terms of only the action of a fixed Hall -subgroup of on a set of normal -sections of . As a consequence, we obtain that divides whenever is a subgroup of a finite -separable group . This generalizes a recent result of Navarro. In addition, our method gives an alternative proof of Navarro's result.
3.
R. C. Brown 《Proceedings of the American Mathematical Society》2004,132(8):2273-2280
Using a recent result of Chernyavskaya and Shuster we show that the maximal operator determined by on , -\infty$">, where and the mean value of computed over all subintervals of of a fixed length is bounded away from zero, shares several standard ``limit-point at " properties of the case. We also show that there is a unique solution of that is in all , .
4.
Sandy Grabiner 《Proceedings of the American Mathematical Society》2004,132(6):1675-1684
Suppose that is a weighted convolution algebra on with the weight normalized so that the corresponding space of measures is the dual space of the space of continuous functions. Suppose that is a continuous nonzero homomorphism, where is also a convolution algebra. If is norm dense in , we show that is (relatively) weak dense in , and we identify the norm closure of with the convergence set for a particular semigroup. When is weak continuous it is enough for to be weak dense in . We also give sufficient conditions and characterizations of weak continuity of . In addition, we show that, for all nonzero in , the sequence converges weak to 0. When is regulated, converges to 0 in norm.
5.
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.
6.
U. K. Anandavardhanan Anthony C. Kable R. Tandon 《Proceedings of the American Mathematical Society》2004,132(10):2875-2883
Let be a quadratic extension of -adic fields. If is an admissible representation of that is parabolically induced from discrete series representations, then we prove that the space of -invariant linear functionals on has dimension one, where is the mirabolic subgroup. As a corollary, it is deduced that if is distinguished by , then the twisted tensor -function associated to has a pole at . It follows that if is a discrete series representation, then at most one of the representations and is distinguished, where is an extension of the local class field theory character associated to . This is in agreement with a conjecture of Flicker and Rallis that relates the set of distinguished representations with the image of base change from a suitable unitary group.
7.
Jie-Hua Mai 《Proceedings of the American Mathematical Society》2004,132(9):2761-2767
Let be a complete metric space without isolated points, and let be a continuous map. In this paper we prove that if is transitive and has a periodic point of period , then has a scrambled set consisting of transitive points such that each is a synchronously proximal Cantor set, and is dense in . Furthermore, if is sensitive (for example, if is chaotic in the sense of Devaney), with being a sensitivity constant, then this is an -scrambled set.
8.
Zhe Dong 《Proceedings of the American Mathematical Society》2004,132(8):2257-2263
Suppose that is admissible. It is shown that the convex hull of unitary elements of a weakly closed -module contains the whole unit ball of if and only if and for any 0$">, 0$">.
9.
Colin C. Graham 《Proceedings of the American Mathematical Society》2004,132(7):1963-1971
Theorem. If are perfect compact subsets of the locally compact metrizable abelian group, then there are pairwise disjoint perfect subsets such that (i) is either a Kronecker set or (ii) for some , is a translate of a -set all of whose elements have order , and (iii) is isomorphic to the projective tensor product .
This extends what was previously known for groups such as or for the case to the general locally compact abelian group. Old results concerning the local existence of Kronecker and -sets are improved.
10.
Mamoru Furuya Hiroshi Niitsuma 《Proceedings of the American Mathematical Society》2004,132(11):3189-3193
We introduce the concept of -adic -basis as an extension of the concept of -basis. Let be a regular local ring of prime characteristic and a ring such that . Then we prove that is a regular local ring if and only if there exists an -adic -basis of and is Noetherian.