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1.
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.
2.
Jon P. Bannon 《Proceedings of the American Mathematical Society》2005,133(3):835-840
We introduce a notion of transitive family of subspaces relative to a type factor, and hence a notion of transitive family of projections in such a factor. We show that whenever is a factor of type and is generated by two self-adjoint elements, then contains a transitive family of projections. Finally, we exhibit a free transitive family of projections that generate a factor of type .
3.
Kok Seng Chua 《Proceedings of the American Mathematical Society》2005,133(3):661-670
We introduce a family of bi-dimensional theta functions which give uniformly explicit formulae for the theta series of hermitian lattices over imaginary quadratic fields constructed from codes over and , and give an interesting geometric characterization of the theta series that arise in terms of the basic strongly modular lattice . We identify some of the hermitian lattices constructed and observe an interesting pair of nonisomorphic 3/2 dimensional codes over that give rise to isomorphic hermitian lattices when constructed at the lowest level 7 but nonisomorphic lattices at higher levels. The results show that the two alphabets and are complementary and raise the natural question as to whether there are other such complementary alphabets for codes.
4.
Dong Zhe 《Proceedings of the American Mathematical Society》2005,133(6):1629-1637
In this paper we prove that for any unital -weakly closed algebra which is -weakly generated by finite-rank operators in , every -weakly closed -submodule has . In the case of nest algebras, if are nests, we obtain the following -fold tensor product formula:
where each is the -weakly closed Alg -submodule determined by an order homomorphism from into itself.
where each is the -weakly closed Alg -submodule determined by an order homomorphism from into itself.
5.
Caishi Wang Zhiyuan Huang Xiangjun Wang 《Proceedings of the American Mathematical Society》2005,133(3):891-898
Let be the canonical framework of white noise analysis over the Gel'fand triple and be the space of continuous linear operators from to . Let be a self-adjoint operator in with spectral representation . In this paper, it is proved that under appropriate conditions upon , there exists a unique linear mapping such that for each . The mapping is then naturally used to define as , where is the Dirac -function. Finally, properties of the mapping are investigated and several results are obtained.
6.
Stefan Friedl 《Proceedings of the American Mathematical Society》2005,133(3):647-653
Let be a number field closed under complex conjugation. Denote by the Witt group of hermitian forms over . We find full invariants for detecting non-zero elements in . This group plays an important role in topology in the work done by Casson and Gordon.
7.
Richard Aron V. I. Gurariy J. B. Seoane 《Proceedings of the American Mathematical Society》2005,133(3):795-803
We show that there is an infinite-dimensional vector space of differentiable functions on every non-zero element of which is nowhere monotone. We also show that there is a vector space of dimension of functions every non-zero element of which is everywhere surjective.
8.
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.
9.
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.
10.
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.
11.
Yifeng Xue 《Proceedings of the American Mathematical Society》2007,135(3):705-711
A unital -algebra is said to have the (APD)-property if every nonzero element in has the approximate polar decomposition. Let be a closed ideal of . Suppose that and have (APD). In this paper, we give a necessary and sufficient condition that makes have (APD). Furthermore, we show that if and or is a simple purely infinite -algebra, then has (APD).
12.
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.
13.
Olga Holtz 《Proceedings of the American Mathematical Society》2005,133(3):711-717
Newton's inequalities are shown to hold for the normalized coefficients of the characteristic polynomial of any - or inverse -matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. They are also used to derive some new necessary conditions on the eigenvalues of nonnegative matrices.
14.
Paul A. Hagelstein Roger L. Jones 《Proceedings of the American Mathematical Society》2005,133(1):185-190
Let denote the unit circle. An example of a sublinear translation-invariant operator acting on is given such that is of restricted weak type but not of weak type .
15.
Frank Sottile Thorsten Theobald 《Proceedings of the American Mathematical Society》2005,133(10):2835-2844
Let and denote the dimension and the degree of the Grassmannian , respectively. For each there are (a priori complex) -planes in tangent to general quadratic hypersurfaces in . We show that this class of enumerative problems is fully real, i.e., for there exists a configuration of real quadrics in (affine) real space so that all the mutually tangent -flats are real.
16.
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 .
17.
David Schrittesser 《Proceedings of the American Mathematical Society》2007,135(4):1213-1222
-absoluteness for forcing means that for any forcing , . `` inaccessible to reals' means that for any real , . To measure the exact consistency strength of `` -absoluteness for forcing and is inaccessible to reals', we introduce a weak version of a weakly compact cardinal, namely, a (lightface) -indescribable cardinal; has this property exactly if it is inaccessible and .
18.
John Kulesza 《Proceedings of the American Mathematical Society》2005,133(3):899-904
We extend the technique of Mrowka to show that his space has the property that dim while ind , assuming his extra set-theoretic hypothesis. We also show that is compact, so assuming the extra axiom, there is an compact metric space with no compact completion.
19.
Janko Marovt 《Proceedings of the American Mathematical Society》2006,134(4):1065-1075
Let be a compact Hausdorff space which satisfies the first axiom of countability, let and let , be the set of all continuous functions from to If , ,is a bijective multiplicative map, then there exist a homeomorphism and a continuous map such that for all and for all
20.
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 .