共查询到20条相似文献,搜索用时 250 毫秒
1.
Given a decreasing weight and an Orlicz function satisfying the -condition at zero, we show that the Orlicz-Lorentz sequence space contains an -isomorphic copy of , if and only if the Orlicz sequence space does, that is, if , where and are the Matuszewska-Orlicz lower and upper indices of , respectively. If does not satisfy the -condition, then a similar result holds true for order continuous subspaces and of and , respectively.
2.
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.
3.
John R. Klein 《Proceedings of the American Mathematical Society》2006,134(6):1825-1833
For a Poincaré duality space and a map , consider the homotopy fiber product . If is orientable with respect to a multiplicative cohomology theory , then, after suitably regrading, it is shown that the -homology of has the structure of a graded associative algebra. When is the diagonal map of a manifold , one recovers a result of Chas and Sullivan about the homology of the unbased loop space .
4.
Gabriel Navarro Pham Huu Tiep 《Proceedings of the American Mathematical Society》2006,134(10):2833-2837
If is a prime number and is a finite group, we show that has an irreducible complex character of degree not divisible by with values in the cyclotomic field .
5.
T. Kalmes 《Proceedings of the American Mathematical Society》2006,134(10):2997-3002
A -semigroup on a Banach space is called hypercyclic if there exists an element such that is dense in . is called chaotic if is hypercyclic and the set of its periodic vectors is dense in as well. We show that a spectral condition introduced by Desch, Schappacher and Webb requiring many eigenvectors of the generator which depend analytically on the eigenvalues not only implies the chaoticity of the semigroup but the chaoticity of every . Furthermore, we show that semigroups whose generators have compact resolvent are never chaotic. In a second part we prove the existence of hypercyclic vectors in for a hypercyclic semigroup , where is its generator.
6.
Sangyop Lee 《Proceedings of the American Mathematical Society》2006,134(9):2767-2770
We show that if a hyperbolic -manifold with a union of tori admits two annular Dehn fillings at distance , then is bounded by at most three tori.
7.
Danny Calegari Nathan M. Dunfield 《Proceedings of the American Mathematical Society》2006,134(11):3131-3136
We give an example of a subgroup of which is a strictly ascending HNN extension of a non-abelian finitely generated free group . In particular, we exhibit a free group in of rank which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir (2005). The main ingredient in our construction is a specific finite volume (non-compact) hyperbolic 3-manifold which is a surface bundle over the circle. In particular, most of comes from the fundamental group of a surface fiber. A key feature of is that there is an element of in with an eigenvalue which is the square root of a rational integer. We also use the Bass-Serre tree of a field with a discrete valuation to show that the group we construct is actually free.
8.
Jack Sonn 《Proceedings of the American Mathematical Society》2008,136(6):1955-1960
Let be a monic polynomial in with no rational roots but with roots in for all , or equivalently, with roots mod for all . It is known that cannot be irreducible but can be a product of two or more irreducible polynomials, and that if is a product of irreducible polynomials, then its Galois group must be a union of conjugates of proper subgroups. We prove that for any , every finite solvable group that is a union of conjugates of proper subgroups (where all these conjugates have trivial intersection) occurs as the Galois group of such a polynomial, and that the same result (with ) holds for all Frobenius groups. It is also observed that every nonsolvable Frobenius group is realizable as the Galois group of a geometric, i.e. regular, extension of .
9.
Suppose that is a -dynamical system such that is of polynomial growth. If is finite dimensional, we show that any element in has slow growth and that is -regular. Furthermore, if is discrete and is a ``nice representation' of , we define a new Banach -algebra which coincides with when is finite dimensional. We also show that any element in has slow growth and is -regular.
10.
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.
11.
Gré gory Ginot Gilles Halbout 《Proceedings of the American Mathematical Society》2006,134(3):621-630
Let be the Hochschild complex of cochains on and let be the space of multivector fields on . In this paper we prove that given any -structure (i.e. Gerstenhaber algebra up to homotopy structure) on , and any -morphism (i.e. morphism of a commutative, associative algebra up to homotopy) between and , there exists a -morphism between and that restricts to . We also show that any -morphism (i.e. morphism of a Lie algebra up to homotopy), in particular the one constructed by Kontsevich, can be deformed into a -morphism, using Tamarkin's method for any -structure on . We also show that any two of such -morphisms are homotopic.
12.
Michael Ray Oliver 《Proceedings of the American Mathematical Society》2006,134(8):2419-2425
The Borel cardinality of the quotient of the power set of the natural numbers by the ideal of asymptotically zero-density sets is shown to be the same as that of the equivalence relation induced by the classical Banach space . We also show that a large collection of ideals introduced by Louveau and Velickovic, with pairwise incomparable Borel cardinality, are all Borel reducible to . This refutes a conjecture of Hjorth and has facilitated further work by Farah.
13.
Let , , , , be the usual operators on classes of rings: and for isomorphic and homomorphic images of rings and , , respectively for subrings, direct, and subdirect products of rings. If is a class of commutative rings with identity (and in general of any kind of algebraic structures), then the class is known to be the variety generated by the class . Although the class is in general a proper subclass of the class for many familiar varieties . Our goal is to give an example of a class of commutative rings with identity such that . As a consequence we will describe the structure of two partially ordered monoids of operators.
14.
Detlev W. Hoffmann 《Proceedings of the American Mathematical Society》2006,134(3):645-652
Let be a field of characteristic and let be a purely inseparable extension of exponent . We determine the kernel of the natural restriction map between the Witt rings of bilinear forms of and , respectively. This complements a result by Laghribi who computed the kernel for the Witt groups of quadratic forms for such an extension . Based on this result, we will determine for a wide class of finite extensions which are not necessarily purely inseparable.
15.
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.
16.
Wlodzimierz Bak Andrzej Hulanicki 《Proceedings of the American Mathematical Society》2006,134(5):1467-1472
We prove that the spectrum of a convolution operator on a locally compact group by a self-adjoint -function is the same on and and consequently on all spaces, if and only if a Beurling algebra contains non-analytic functions on operating on into .
17.
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 .
18.
Kenneth M. Monks 《Proceedings of the American Mathematical Society》2006,134(10):2861-2872
Define by if is odd and if is even. The Conjecture states that the -orbit of every positive integer contains . A set of positive integers is said to be sufficient if the -orbit of every positive integer intersects the -orbit of an element of that set. Thus to prove the Conjecture it suffices to prove it on some sufficient set. Andaloro proved that the sets are sufficient for and asked if is also sufficient for larger values of . We answer this question in the affirmative by proving the stronger result that is sufficient for any nonnegative integers and with i.e. every nonconstant arithmetic sequence forms a sufficient set. We then prove analagous results for the Divergent Orbits Conjecture and Nontrivial Cycles Conjecture.
19.
Let be a compact connected orientable Riemannian manifold of dimension and let be the -th positive eigenvalue of the Laplacian acting on differential forms of degree on . We prove that the metric can be conformally deformed to a metric , having the same volume as , with arbitrarily large for all .
Note that for the other values of , that is and , one can deduce from the literature that, 0$">, the -th eigenvalue is uniformly bounded on any conformal class of metrics of fixed volume on .
For , we show that, for any positive integer , there exists a metric conformal to such that, , , that is, the first eigenforms of are all exact forms.
20.
Xian-Jin Li 《Proceedings of the American Mathematical Society》2008,136(6):1945-1953
An explicit Dirichlet series is obtained, which represents an analytic function of in the half-plane except for having simple poles at points that correspond to exceptional eigenvalues of the non-Euclidean Laplacian for Hecke congruence subgroups by the relation for . Coefficients of the Dirichlet series involve all class numbers of real quadratic number fields. But, only the terms with for sufficiently large discriminants contribute to the residues of the Dirichlet series at the poles , where is the multiplicity of the eigenvalue for . This may indicate (I'm not able to prove yet) that the multiplicity of exceptional eigenvalues can be arbitrarily large. On the other hand, by density theorem the multiplicity of exceptional eigenvalues is bounded above by a constant depending only on .