共查询到20条相似文献,搜索用时 31 毫秒
1.
Muharem Avdispahic Lejla Smajlovic 《Proceedings of the American Mathematical Society》2006,134(7):2125-2130
A. Magyar's result on -bounds for a family of operators on -spheres () in is improved to match the corresponding theorem for -spheres.
2.
Yuming Liu 《Proceedings of the American Mathematical Society》2006,134(6):1605-1613
Let and be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence between and such that is induced by exact functors. We present a nice correspondence between indecomposable modules over and . As a consequence, we have the following: (1) If is a self-injective algebra, then so is ; (2) If and are finite dimensional algebras over an algebraically closed field , and if is of finite representation type such that the Auslander-Reiten quiver of has no oriented cycles, then and are Morita equivalent.
3.
David H. Bailey Michal Misiurewicz 《Proceedings of the American Mathematical Society》2006,134(9):2495-2501
A real number is said to be -normal if every -long string of digits appears in the base- expansion of with limiting frequency . We prove that is -normal if and only if it possesses no base- ``hot spot'. In other words, is -normal if and only if there is no real number such that smaller and smaller neighborhoods of are visited by the successive shifts of the base- expansion of with larger and larger frequencies, relative to the lengths of these neighborhoods.
4.
We prove that all -cotilting -modules are pure-injective for any ring and any . To achieve this, we prove that is a covering class whenever is an -module such that is closed under products and pure submodules.
5.
I. M. Isaacs Thomas Michael Keller U. Meierfrankenfeld Alexander Moretó 《Proceedings of the American Mathematical Society》2006,134(11):3123-3130
Let be a finite group that acts on a nonzero finite dimensional vector space over an arbitrary field. Assume that is completely reducible as a -module, and that fixes no nonzero vector of . We show that some element has a small fixed-point space in . Specifically, we prove that we can choose so that , where is the smallest prime divisor of .
6.
Joachim Zacharias 《Proceedings of the American Mathematical Society》2006,134(7):1909-1916
Recently J.Roe considered the question of whether for a discrete group the reduced group -algebra is the fixed point algebra of Ad acting on the uniform Roe algebra . is said to have the invariant translation approximation property in this case. We consider a slight generalization of this property which, for exact , is equivalent to the operator space approximation property of . We also give a new characterization of exactness and a short proof of the equivalence of exactness of and exactness of for discrete groups.
7.
Zhiguo Hu 《Proceedings of the American Mathematical Society》2006,134(10):3085-3095
Let be the Fourier algebra of a locally compact group and the -algebra of uniformly continuous linear functionals on . We study how the centre problem for the algebra (resp. ) is related to the centre problem for the algebras (resp. ) of -compact open subgroups of . We extend some results of Lau-Losert on the centres of and .
8.
T. S. S. R. K. Rao 《Proceedings of the American Mathematical Society》2006,134(7):2079-2082
In this paper we generalize a result of Hopenwasser and Plastiras (1997) that gives a geometric condition under which into isometries from to have a unique extension to an isometry in . We show that when and are separable reflexive Banach spaces having the metric approximation property with strictly convex and smooth and such that is a Hahn-Banach smooth subspace of , any nice into isometry has a unique extension to an isometry in .
9.
It is shown that an operator on the Hardy space (or ) commutes with all analytic Toeplitz operators modulo the finite rank operators if and only if . Here is a finite rank operator, and in the case , is a sum of a rational function and a bounded analytic function, and in the case , is a bounded analytic function.
10.
Esther Beneish 《Proceedings of the American Mathematical Society》2006,134(7):1869-1873
Let be a prime greater than , and let be the semi-direct product of a group of order by a cyclic group of order , which acts faithfully on . Let be the localization of at . We show that the Krull-Schmidt Theorem fails for the category of invertible -lattices.
11.
Kamran Divaani-Aazar Mohammad Ali Esmkhani Massoud Tousi 《Proceedings of the American Mathematical Society》2006,134(10):2817-2822
Let be a commutative ring with identity and an -module. It is shown that if is pure injective, then is isomorphic to a direct summand of the direct product of a family of finitely embedded modules. As a result, it follows that if is Noetherian, then is pure injective if and only if is isomorphic to a direct summand of the direct product of a family of Artinian modules. Moreover, it is proved that is pure injective if and only if there is a family of -algebras which are finitely presented as -modules, such that is isomorphic to a direct summand of a module of the form , where for each , is an injective -module.
12.
Desmond Sheiham 《Proceedings of the American Mathematical Society》2006,134(12):3465-3474
If is a triangular matrix ring, the columns and are f.g. projective -modules. We describe the universal localization of which makes invertible an -module morphism , generalizing a theorem of A. Schofield. We also describe the universal localization of -modules.
13.
Ping Wong Ng 《Proceedings of the American Mathematical Society》2006,134(8):2223-2228
Let be a unital, simple, separable -algebra with real rank zero, stable rank one, and weakly unperforated ordered group. Suppose, also, that can be locally approximated by type I algebras with Hausdorff spectrum and bounded irreducible representations (the bound being dependent on the local approximating algebra). Then is tracially approximately finite dimensional (i.e., has tracial rank zero).
Hence, is an -algebra with bounded dimension growth and is determined by -theoretic invariants.
The above result also gives the first proof for the locally case.
14.
Bin Han 《Proceedings of the American Mathematical Society》2006,134(7):1973-1983
Let be a compactly supported refinable function in such that the shifts of are stable and for a -periodic trigonometric polynomial . A wavelet function can be derived from by . If is an orthogonal refinable function, then it is well known that generates an orthonormal wavelet basis in . Recently, it has been shown in the literature that if is a -spline or pseudo-spline refinable function, then always generates a Riesz wavelet basis in . It was an open problem whether can always generate a Riesz wavelet basis in for any compactly supported refinable function in with stable shifts. In this paper, we settle this problem by proving that for a family of arbitrarily smooth refinable functions with stable shifts, the derived wavelet function does not generate a Riesz wavelet basis in . Our proof is based on some necessary and sufficient conditions on the -periodic functions and in such that the wavelet function , defined by , generates a Riesz wavelet basis in .
15.
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.
16.
Mohamed Ali Toumi 《Proceedings of the American Mathematical Society》2006,134(6):1615-1621
Let be an Archimedean vector lattice, let be its Dedekind completion and let be a Dedekind complete vector lattice. If is an orthosymmetric lattice bimorphism, then there exists a lattice bimorphism that not just extends but also has to be orthosymmetric. As an application, we prove the following: Let be an Archimedean -algebra. Then the multiplication in can be extended to a multiplication in , the Dedekind completion of , in such a fashion that is again a -algebra with respect to this extended multiplication. This gives a positive answer to the problem posed by C. B. Huijsmans in 1990.
17.
Amir Akbary 《Proceedings of the American Mathematical Society》2006,134(11):3143-3151
Let be a newform of even weight , level and character and let be a newform of even weight , level and character . We give a generalization of a theorem of Elliott, regarding the average values of Dirichlet -functions, in the context of twisted modular -functions associated to and . Using this result, we find a lower bound in terms of for the number of primitive Dirichlet characters modulo prime whose twisted product -functions are non-vanishing at a fixed point with .
18.
Gerald Schmieder 《Proceedings of the American Mathematical Society》2006,134(12):3605-3611
For a closed nowhere dense subset of a bounded univalent holomorphic function on is found such that equals the cluster set of its fixed points.
19.
Bo-Hae Im 《Proceedings of the American Mathematical Society》2006,134(6):1623-1630
Let be a number field, an algebraic closure of , the absolute Galois group , the maximal abelian extension of and an elliptic curve defined over . In this paper, we prove that if all 2-torsion points of are -rational, then for each , has infinite rank, and hence has infinite rank.
20.
Florin Panaite Freddy Van Oystaeyen 《Proceedings of the American Mathematical Society》2007,135(6):1669-1677
If is a quasi-Hopf algebra and is a right -comodule algebra such that there exists a morphism of right -comodule algebras, we prove that there exists a left -module algebra such that . The main difference when comparing to the Hopf case is that, from the multiplication of , which is associative, we have to obtain the multiplication of , which in general is not; for this we use a canonical projection arising from the fact that becomes a quasi-Hopf -bimodule.