共查询到20条相似文献,搜索用时 31 毫秒
1.
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.
2.
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$">, 0$">.
3.
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.
4.
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.
5.
Applying the density theorem on algebras with -derivations, we show that if a -derivation of a unital Banach algebra is spectrally bounded, then . Also, if and only if , where denotes the spectral radius of .
6.
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.
7.
Jesper Tidblom 《Proceedings of the American Mathematical Society》2004,132(8):2265-2271
The aim of this article is to prove a Hardy-type inequality, concerning functions in for some domain , involving the volume of and the distance to the boundary of . The inequality is a generalization of a recently proved inequality by M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and A. Laptev (2002), which dealt with the special case .
8.
Huaquan Wei Yanming Wang Yangming Li 《Proceedings of the American Mathematical Society》2004,132(8):2197-2204
This paper proves: Let be a saturated formation containing . Suppose that is a group with a normal subgroup such that .
(1) If all maximal subgroups of any Sylow subgroup of are -supple- mented in , then ;
(2) If all minimal subgroups and all cyclic subgroups with order 4 of are -supplemented in , then .
9.
L. Herná ndez Encinas J. Muñ oz Masqué 《Proceedings of the American Mathematical Society》2004,132(7):2127-2132
A classical result by J. W. Milnor states that the total curvature of a closed curve in the Euclidean -space is the limit of the total curvatures of polygons inscribed in . In the present paper a similar geometric interpretation is given for all total curvatures , .
10.
Sergei V. Astashkin Lech Maligranda 《Proceedings of the American Mathematical Society》2004,132(10):2929-2938
We show that if is a rearrangement invariant space on that is an interpolation space between and and for which we have only a one-sided estimate of the Boyd index 1/p, 1 < p < \infty$">, then is an interpolation space between and . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type .
11.
Sandy Grabiner 《Proceedings of the American Mathematical Society》2004,132(6):1675-1684
Suppose that is a weighted convolution algebra on with the weight normalized so that the corresponding space of measures is the dual space of the space of continuous functions. Suppose that is a continuous nonzero homomorphism, where is also a convolution algebra. If is norm dense in , we show that is (relatively) weak dense in , and we identify the norm closure of with the convergence set for a particular semigroup. When is weak continuous it is enough for to be weak dense in . We also give sufficient conditions and characterizations of weak continuity of . In addition, we show that, for all nonzero in , the sequence converges weak to 0. When is regulated, converges to 0 in norm.
12.
Tavan T. Trent 《Proceedings of the American Mathematical Society》2004,132(8):2429-2432
We find the maximal invariant subspaces for on -valued Bergman-type spaces.
13.
We prove that there are many -degrees in the random reals.
14.
Mark Tomforde 《Proceedings of the American Mathematical Society》2004,132(6):1787-1795
We characterize stability of graph -algebras by giving five conditions equivalent to their stability. We also show that if is a graph with no sources, then is stable if and only if each vertex in can be reached by an infinite number of vertices. We use this characterization to realize the stabilization of a graph -algebra. Specifically, if is a graph and is the graph formed by adding a head to each vertex of , then is the stabilization of ; that is, .
15.
Let 1$"> be a Pisot unit. A family of sets defined by a -numeration system has been extensively studied as an atomic surface or Rauzy fractal. For the purpose of constructing a Markov partition, a domain constructed by an atomic surface has appeared in several papers. In this paper we show that the domain completely characterizes the set of purely periodic -expansions.
16.
Krzysztof Ciesielski Janusz Pawlikowski 《Proceedings of the American Mathematical Society》2004,132(11):3379-3385
We prove that the Covering Property Axiom CPA , which holds in the iterated perfect set model, implies the following facts.
- If is an intersection of -many open sets of a Polish space and has cardinality continuum, then contains a perfect set.
- There exists a subset of the Cantor set which is an intersection of -many open sets but is not a union of -many closed sets.
17.
A. Picó n C. Piñ eiro 《Proceedings of the American Mathematical Society》2004,132(10):2893-2898
Let a Banach space and a -algebra of subsets of a set . We say that a vector measure Banach space has the bounded Vitaly-Hahn-Sacks Property if it satisfies the following condition: Every vector measure , for which there exists a bounded sequence in verifying for all , must belong to . Among other results, we prove that, if is a vector measure Banach space with the bounded V-H-S Property and containing a complemented copy of , then contains a copy of .
18.
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.
19.
Vassilis Kanellopoulos 《Proceedings of the American Mathematical Society》2004,132(11):3231-3242
W. T. Gowers' theorem asserts that for every Lipschitz function and 0$">, there exists an infinite-dimensional subspace of such that the oscillation of on is at most . The proof of this theorem has been reduced by W. T. Gowers to the proof of a new Ramsey type theorem. Our aim is to present a proof of the last result.
20.
Z. Ercan 《Proceedings of the American Mathematical Society》2004,132(6):1761-1763
We prove that for a compact Hausdorff space without isolated points, and are isometrically Riesz isomorphic spaces under a certain topology on . Moreover, is a closed subspace of . This provides concrete examples of compact Hausdorff spaces such that the Dedekind completion of is (= the set of all bounded real-valued functions on ) since the Dedekind completion of is ( and spaces as Banach lattices).