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1.
We prove two theorems linking the cohomology of a pro- group with the conjugacy classes of its finite subgroups.
The number of conjugacy classes of elementary abelian -subgroups of is finite if and only if the ring is finitely generated modulo nilpotent elements.
If the ring is finitely generated, then the number of conjugacy classes of finite subgroups of is finite.
2.
Xavier Massaneda Pascal J. Thomas 《Proceedings of the American Mathematical Society》2000,128(3):837-843
We show that a sequence in the unit ball of is sampling for the Hardy spaces , , if and only if the admissible accumulation set of in the unit sphere has full measure. For the situation is quite different. While this condition is still sufficient, when (in contrast to the one dimensional situation) there exist sampling sequences for whose admissible accumulation set has measure 0. We also consider the sequence obtained by applying to each a random rotation, and give a necessary and sufficient condition on so that, with probability one, is of sampling for , .
3.
Yves Fé lix Jean-Claude Thomas 《Proceedings of the American Mathematical Society》2004,132(1):305-312
Let be a simply-connected closed oriented -dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras where is the loop algebra defined by Chas and Sullivan. As usual denotes the monoid of self-equivalences homotopic to the identity, and the space of based loops. When is of characteristic zero, yields isomorphisms where denotes the Hodge decomposition on .
4.
Andreas Defant Mieczyslaw Mastylo Carsten Michels 《Proceedings of the American Mathematical Society》2004,132(2):513-521
Using abstract interpolation theory, we study eigenvalue distribution problems for operators on complex symmetric Banach sequence spaces. More precisely, extending two well-known results due to König on the asymptotic eigenvalue distribution of operators on -spaces, we prove an eigenvalue estimate for Riesz operators on -spaces with , which take values in a -concave symmetric Banach sequence space , as well as a dual version, and show that each operator on a -convex symmetric Banach sequence space , which takes values in a -concave symmetric Banach sequence space , is a Riesz operator with a sequence of eigenvalues that forms a multiplier from into . Examples are presented which among others show that the concavity and convexity assumptions are essential.
5.
A. S. Kleshchev A. E. Zalesski 《Proceedings of the American Mathematical Society》2004,132(6):1605-1612
Let be an algebraically closed field of characteristic 0$"> and let be a quasi-simple group with . We describe the minimal polynomials of elements of order in irreducible representations of over . If , we determine the minimal polynomials of elements of order in -modular irreducible representations of , , , , , and .
6.
Andreas Weiermann 《Proceedings of the American Mathematical Society》2004,132(2):553-561
Let be a number-theoretic function. A finite set of natural numbers is called -large if . Let be the Paris Harrington statement where we replace the largeness condition by a corresponding -largeness condition. We classify those functions for which the statement is independent of first order (Peano) arithmetic . If is a fixed iteration of the binary length function, then is independent. On the other hand is provable in . More precisely let where denotes the -times iterated binary length of and denotes the inverse function of the -th member of the Hardy hierarchy. Then is independent of (for ) iff .
7.
Edward Bierstone 《Proceedings of the American Mathematical Society》2004,132(4):997-1003
Let : denote a real analytic function on an open subset of , and let denote the points where does not admit a local analytic extension. We show that if is semialgebraic (respectively, globally subanalytic), then is semialgebraic (respectively, subanalytic) and extends to a semialgebraic (respectively, subanalytic) neighbourhood of . (In the general subanalytic case, is not necessarily subanalytic.) Our proof depends on controlling the radii of convergence of power series centred at points in the image of an analytic mapping , in terms of the radii of convergence of at points , where denotes the Taylor expansion of at .
8.
Let be a nonempty closed convex subset of a real Banach space and be a Lipschitz pseudocontractive self-map of with . An iterative sequence is constructed for which as . If, in addition, is assumed to be bounded, this conclusion still holds without the requirement that Moreover, if, in addition, has a uniformly Gâteaux differentiable norm and is such that every closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then the sequence converges strongly to a fixed point of . Our iteration method is of independent interest.
9.
Robert M. Guralnick Gunter Malle Gabriel Navarro 《Proceedings of the American Mathematical Society》2004,132(4):973-979
Using the classification of finite simple groups we prove the following statement: Let 3$"> be a prime, a group of automorphisms of -power order of a finite group , and a -invariant Sylow -subgroup of . If is trivial, then is solvable. An equivalent formulation is that if has a self-normalizing Sylow -subgroup with 3$"> a prime, then is solvable. We also investigate the possibilities when .
10.
Suhas Nayak 《Proceedings of the American Mathematical Society》2004,132(1):33-35
This paper extends a result obtained by Wigner and von Neumann. We prove that a non-constant real-valued function, , in where is an interval of the real line, is a monotone matrix function of order on if and only if a related, modified function is a monotone matrix function of order for every value of in , assuming that is strictly positive on .
11.
Enrico Leuzinger 《Proceedings of the American Mathematical Society》2004,132(3):919-927
Let be a noncompact semisimple Lie group and an arbitrary discrete, torsion-free subgroup of . Let be the bottom of the spectrum of the Laplace-Beltrami operator on the locally symmetric space , and let be the exponent of growth of . If has rank , then these quantities are related by a well-known formula due to Elstrodt, Patterson, Sullivan and Corlette. In this note we generalize that relation to the higher rank case by estimating from above and below by quadratic polynomials in . As an application we prove a rigiditiy property of lattices.
12.
A. Chigogidze A. Karasev M. Rø rdam 《Proceedings of the American Mathematical Society》2004,132(3):783-788
It is proved that if is a compact Hausdorff space of Lebesgue dimension , then the squaring mapping , defined by , is open if and only if . Hence the Lebesgue dimension of can be detected from openness of the squaring maps . In the case it is proved that the map , from the selfadjoint elements of a unital -algebra into its positive elements, is open if and only if is isomorphic to for some compact Hausdorff space with .
13.
Flavio Abdenur Artur Avila Jairo Bochi 《Proceedings of the American Mathematical Society》2004,132(3):699-705
We prove that nontrivial homoclinic classes of -generic flows are topologically mixing. This implies that given , a nontrivial -robustly transitive set of a vector field , there is a -perturbation of such that the continuation of is a topologically mixing set for . In particular, robustly transitive flows become topologically mixing after -perturbations. These results generalize a theorem by Bowen on the basic sets of generic Axiom A flows. We also show that the set of flows whose nontrivial homoclinic classes are topologically mixing is not open and dense, in general.
14.
Herbert Weigel 《Proceedings of the American Mathematical Society》2004,132(6):1775-1778
Let be a Banach algebra, , the spectrum of and the spectral abscissa of . If , then we show that there exists an algebra cone such that is exponentially nonnegative with respect to and the spectral radius is increasing on .
15.
Let be a nondegenerate coaction of on a -algebra , and let be a closed subgroup of . The dual action is proper and saturated in the sense of Rieffel, and the generalised fixed-point algebra is the crossed product of by the homogeneous space . The resulting Morita equivalence is a version of Mansfield's imprimitivity theorem which requires neither amenability nor normality of .
16.
Wen-Fong Ke Bing-Ren Li Ngai-Ching Wong 《Proceedings of the American Mathematical Society》2004,132(7):1979-1985
Let be locally compact Hausdorff spaces and , be Banach algebras. Let be a zero product preserving bounded linear map with dense range. We show that is given by a continuous field of algebra homomorphisms from into if is irreducible. As corollaries, such a surjective arises from an algebra homomorphism, provided that is a -algebra and is a semi-simple Banach algebra, or both and are -algebras.
17.
D. S. Passman 《Proceedings of the American Mathematical Society》2004,132(1):37-46
Let be a commutative integral domain of characteristic , and let be a finite subgroup of , the projective general linear group of degree over . In this note, we show that if , then also contains the free product , where is the infinite cyclic group generated by the image of a suitable transvection.
18.
Teresa Crespo 《Proceedings of the American Mathematical Society》2004,132(3):691-695
We present an explicit construction of the complete family of Galois extensions of a field of characteristic 3 with Galois group the central product of a double cover of the symmetric group and the quaternion group , containing a given -extension of the field .
19.
Igor Fulman Paul S. Muhly Dana P. Williams 《Proceedings of the American Mathematical Society》2004,132(3):707-717
Let be a second countable, locally compact groupoid with Haar system, and let be a bundle of -algebras defined over the unit space of on which acts continuously. We determine conditions under which the associated crossed product is a continuous trace -algebra.
20.
Pamela B. Pierce Daniel Waterman 《Proceedings of the American Mathematical Society》2004,132(3):755-760
The necessary and sufficient condition for to be in the class for every of that class whose range is in the domain of is that be in .