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1.
Artur Hideyuki Tomita 《Proceedings of the American Mathematical Society》2003,131(8):2617-2622
E. K. van Douwen asked in 1980 whether the cardinality of a countably compact group must have uncountable cofinality in . He had shown that this was true under GCH. We answer his question in the negative. V. I. Malykhin and L. B. Shapiro showed in 1985 that under GCH the weight of a pseudocompact group without non-trivial convergent sequences cannot have countable cofinality and showed that there is a forcing model in which there exists a pseudocompact group without non-trivial convergent sequences whose weight is . We show that it is consistent that there exists a countably compact group without non-trivial convergent sequences whose weight is .
2.
Michela Artebani Gian Pietro Pirola 《Proceedings of the American Mathematical Society》2005,133(2):331-341
Let be a compact Riemann surface of genus and be an integer. We show that admits meromorphic functions with monodromy group equal to the alternating group
3.
On subspaces of pseudoradial spaces 总被引:1,自引:0,他引:1
A topological space is pseudoradial if each of its non closed subsets has a sequence (not necessarily with countable length) convergent to outside of . We prove the following results concerning pseudoradial spaces and the spaces , where is an ultrafilter on :
(i) CH implies that, for every ultrafilter on , is a subspace of some regular pseudoradial space.
(ii) There is a model in which, for each P-point , cannot be embedded in a regular pseudoradial space while there is a point such that is a subspace of a zero-dimensional Hausdorff pseudoradial space.
4.
R. Ayala M. Cá rdenas F. F. Lasheras A. Quintero 《Proceedings of the American Mathematical Society》2005,133(5):1527-1535
A finitely presented group is said to be properly -realizable if there exists a compact -polyhedron with and whose universal cover has the proper homotopy type of a (p.l.) -manifold with boundary. In this paper we show that, after taking wedge with a -sphere, this property does not depend on the choice of the compact -polyhedron with . We also show that (i) all -ended and -ended groups are properly -realizable, and (ii) the class of properly -realizable groups is closed under amalgamated free products (HNN-extensions) over a finite cyclic group (as a step towards proving that -ended groups are properly -realizable, assuming -ended groups are).
5.
Xavier Dussau 《Proceedings of the American Mathematical Society》2005,133(5):1379-1386
We prove for some translation-invariant weighted spaces the following characterization: is a multiplier of if and only if leaves invariant every translation-invariant subspace of . This result is equivalent with the reflexivity of the multiplier algebra of .
6.
Spiros A. Argyros Sophocles Mercourakis 《Proceedings of the American Mathematical Society》2005,133(3):773-785
We present two examples of WCG spaces that are not hereditarily WCG. The first is a space with an unconditional basis, and the second is a space such that is WCG and does not contain . The non-WCG subspace of has the additional property that is not WCG and is reflexive.
7.
Carlos Gutierrez Benito Pires 《Proceedings of the American Mathematical Society》2005,133(4):1063-1074
Contrary to the case of vector fields on orientable compact -manifolds, there is a smooth vector field on a non-orientable compact -manifold with a dense orbit (and therefore without closed orbits) whose phase portrait -up to topological equivalence- remains intact under a one-parameter family of twist perturbations localized in a flow box of
8.
Let and be finite groups that have a common central -subgroup for a prime number , and let and respectively be -blocks of and induced by -blocks and respectively of and , both of which have the same defect group. We prove that if and are Morita equivalent via a certain special -bimodule, then such a Morita equivalence lifts to a Morita equivalence between and .
9.
Paul Kirk Charles Livingston 《Proceedings of the American Mathematical Society》2005,133(5):1537-1546
The Hausmann-Weinberger invariant of a group is the minimal Euler characteristic of a closed orientable 4-manifold with fundamental group . We compute this invariant for finitely generated free abelian groups and estimate the invariant for all finitely generated abelian groups.
10.
B. Blackadar recently proved that any full corner in a unital C*-algebra has K-theoretic stable rank greater than or equal to the stable rank of . (Here is a projection in , and fullness means that .) This result is extended to arbitrary (unital) rings in the present paper: If is a full idempotent in , then . The proofs rely partly on algebraic analogs of Blackadar's methods and partly on a new technique for reducing problems of higher stable rank to a concept of stable rank one for skew (rectangular) corners . The main result yields estimates relating stable ranks of Morita equivalent rings. In particular, if where is a finitely generated projective generator, and can be generated by elements, then .
11.
Let be a real Hilbert space. Let , be bounded monotone mappings with , where and are closed convex subsets of satisfying certain conditions. Suppose the equation has a solution in . Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on , and the operators and need not be defined on compact subsets of .
12.
Mariá n Fabian Ondrej F. K. Kalenda Jan Kolá r 《Proceedings of the American Mathematical Society》2005,133(1):295-303
If is an infinite-dimensional Banach space, with separable dual, and is an analytic set such that any point can be reached from by a continuous path contained (except for the point ) in the interior of , then is the range of the derivative of a -smooth function on with bounded nonempty support.
13.
Christoph Schmoeger 《Proceedings of the American Mathematical Society》2005,133(2):511-518
Let be a complex Banach space and a bounded linear operator on . is called meromorphic if the spectrum of is a countable set, with the only possible point of accumulation, such that all the nonzero points of are poles of . By means of the analytical core we give a spectral theory of meromorphic operators. Our results are a generalization of some results obtained by Gong and Wang (2003).
14.
Wieslaw Pawlucki 《Proceedings of the American Mathematical Society》2005,133(2):481-484
For each positive integer we construct a -function of one real variable, the graph of which has the following property: there exists a real function on which is -extendable to , for each finite, but it is not -extendable.
15.
Kamran Divaani-Aazar Amir Mafi 《Proceedings of the American Mathematical Society》2005,133(3):655-660
Let be an ideal of a commutative Noetherian ring and a finitely generated -module. Let be a natural integer. It is shown that there is a finite subset of , such that is contained in union with the union of the sets , where and . As an immediate consequence, we deduce that the first non- -cofinite local cohomology module of with respect to has only finitely many associated prime ideals.
16.
Daniel Azagra Robb Fry Alejandro Montesinos 《Proceedings of the American Mathematical Society》2005,133(3):727-734
We show that if is a separable subspace of a Banach space such that both and the quotient have -smooth Lipschitz bump functions, and is a bounded open subset of , then, for every uniformly continuous function and every 0$">, there exists a -smooth Lipschitz function such that for every .
17.
We prove that any -additive family of sets in an absolutely Souslin metric space has a -discrete refinement provided every partial selector set for is -discrete. As a corollary we obtain that every mapping of a metric space onto an absolutely Souslin metric space, which maps -sets to -sets and has complete fibers, admits a section of the first class. The invariance of Borel and Souslin sets under mappings with complete fibers, which preserves -sets, is shown as an application of the previous result.
18.
Huah Chu Shou-Jen Hu Ming-chang Kang 《Proceedings of the American Mathematical Society》2005,133(10):2865-2871
Let be a linearly reductive group over a field , and let be a -algebra with a rational action of . Given rational --modules and , we define for the induced -action on Hom a generalized Reynolds operator, which exists even if the action on Hom is not rational. Given an -module homomorphism , it produces, in a natural way, an -module homomorphism which is -equivariant. We use this generalized Reynolds operator to study properties of rational - modules. In particular, we prove that if is invariantly generated (i.e. ), then is a projective (resp. flat) -module provided that is a projective (resp. flat) -module. We also give a criterion whether an -projective (or -flat) rational --module is extended from an -module.
19.
Let be a Noetherian homogeneous ring with one-dimensional local base ring . Let be an -primary ideal, let be a finitely generated graded -module and let . Let denote the -th local cohomology module of with respect to the irrelevant ideal 0} R_n$"> of . We show that the first Hilbert-Samuel coefficient of the -th graded component of with respect to is antipolynomial of degree in . In addition, we prove that the postulation numbers of the components with respect to have a common upper bound.
20.
Mohammed Hichem Mortad 《Proceedings of the American Mathematical Society》2005,133(2):455-464
We give classes of unbounded real-valued for which is self-adjoint on , , where is the wave operator defined on .