共查询到20条相似文献，搜索用时 593 毫秒
1.
Let be a compact Hausdorff space and a function algebra. Assume that is the maximal ideal space of . Denoting by the spectrum of an , which in this case coincides with the range of , a result of Molnár is generalized by our Main Theorem: If is a surjective map with the property for every pair of functions , then there exists a homeomorphism such that
for every and every with .
for every and every with .
2.
-weakly closed nest algebra submodules 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.
3.
John A. Baker 《Proceedings of the American Mathematical Society》2005,133(6):1657-1664
Suppose that and are vector spaces over or and are scalar such that whenever We prove that if for and
then each is a ``generalized' polynomial map of ``degree' at most
then each is a ``generalized' polynomial map of ``degree' at most
In case and we show that if some is bounded on a set of positive inner Lebesgue measure, then it is a genuine polynomial function.
Our main aim is to establish the stability of (in the sense of Ulam) in case is a Banach space.
We also solve a distributional analogue of and prove a mean value theorem concerning harmonic functions in two real variables.
4.
We prove the following two theorems.
then .
Theorem 1. Let be a strongly meager subset of . Then it is dual Ramsey null.
We will say that a -ideal of subsets of satisfies the condition iff for every , if
then .
Theorem 2. The -ideals of perfectly meager sets, universally meager sets and perfectly meager sets in the transitive sense satisfy the condition .
5.
Saugata Basu Richard Pollack Marie-Franç oise Roy 《Proceedings of the American Mathematical Society》2005,133(4):965-974
Let be a real closed field and let and be finite subsets of such that the set has elements, the algebraic set defined by has dimension and the elements of and have degree at most . For each we denote the sum of the -th Betti numbers over the realizations of all sign conditions of on by . We prove that
This generalizes to all the higher Betti numbers the bound on . We also prove, using similar methods, that the sum of the Betti numbers of the intersection of with a closed semi-algebraic set, defined by a quantifier-free Boolean formula without negations with atoms of the form or for , is bounded by
making the bound more precise.
This generalizes to all the higher Betti numbers the bound on . We also prove, using similar methods, that the sum of the Betti numbers of the intersection of with a closed semi-algebraic set, defined by a quantifier-free Boolean formula without negations with atoms of the form or for , is bounded by
making the bound more precise.
6.
Cyril Agrafeuil 《Proceedings of the American Mathematical Society》2006,134(11):3287-3294
Let be a sequence of positive real numbers. We define as the space of functions which are analytic in the unit disc , continuous on and such that where is the Fourier coefficient of the restriction of to the unit circle . Let be a closed subset of . We say that is a Beurling-Carleson set if where denotes the distance between and . In 1980, A. Atzmon asked whether there exists a sequence of positive real numbers such that for all and that has the following property: for every Beurling-Carleson set , there exists a non-zero function in that vanishes on . In this note, we give a negative answer to this question.
7.
Hitoshi Tanaka 《Proceedings of the American Mathematical Society》2005,133(3):763-772
Let , , be the Kakeya (Nikodým) maximal operator defined as the supremum of averages over tubes of eccentricity . The (so-called) Fefferman-Stein type inequality:
is shown in the range , where and are some constants depending only on and the dimension and is a weight. The result is a sharp bound up to -factors.
is shown in the range , where and are some constants depending only on and the dimension and is a weight. The result is a sharp bound up to -factors.
8.
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.
9.
Rustam Sadykov 《Proceedings of the American Mathematical Society》2005,133(3):931-936
The Pontrjagin-Thom construction expresses a relation between the oriented bordism groups of framed immersions , and the stable homotopy groups of spheres. We apply the Pontrjagin-Thom construction to the oriented bordism groups of mappings n$">, with mildest singularities. Recently, O. Saeki showed that for , the group is isomorphic to the group of smooth structures on the sphere of dimension . Generalizing, we prove that is isomorphic to the -th stable homotopy group , , where is the group of oriented auto-diffeomorphisms of the sphere and is the group of rotations of .
10.
Igor E. Shparlinski 《Proceedings of the American Mathematical Society》2004,132(10):2817-2824
We consider Gauss sums of the form
with a nontrivial additive character of a finite field of elements of characteristic . The classical bound becomes trivial for . We show that, combining some recent bounds of Heath-Brown and Konyagin with several bounds due to Deligne, Katz, and Li, one can obtain the bound on which is nontrivial for the values of of order up to . We also show that for almost all primes one can obtain a bound which is nontrivial for the values of of order up to .
with a nontrivial additive character of a finite field of elements of characteristic . The classical bound becomes trivial for . We show that, combining some recent bounds of Heath-Brown and Konyagin with several bounds due to Deligne, Katz, and Li, one can obtain the bound on which is nontrivial for the values of of order up to . We also show that for almost all primes one can obtain a bound which is nontrivial for the values of of order up to .
11.
Yun-Zhang Li 《Proceedings of the American Mathematical Society》2005,133(8):2419-2428
The study of Gabor bases of the form for has interested many mathematicians in recent years. Alex Losevich and Steen Pedersen in 1998, Jeffery C. Lagarias, James A. Reeds and Yang Wang in 2000 independently proved that, for any fixed positive integer , is an orthonormal basis for if and only if is a tiling of . Palle E. T. Jorgensen and Steen Pedersen in 1999 gave an explicit characterization of such for , , . Inspired by their work, this paper addresses Gabor orthonormal bases of the form for and some other related problems, where is as above. For a fixed , the generating function of a Gabor orthonormal basis for corresponding to the above is characterized explicitly provided that , which is new even if ; a Shannon type sampling theorem about such is derived when , ; for an arbitrary positive integer , an explicit expression of the with being an orthonormal basis for is obtained under the condition that .
12.
For a -smooth bump function we show that the gradient range is the closure of its interior, provided that admits a modulus of continuity satisfying as . The result is a consequence of a more general result about gradient ranges of bump functions of the same degree of smoothness. For such bump functions we show that for open sets , either the intersection is empty or its topological dimension is at least two. The proof relies on a new Morse-Sard type result where the smoothness hypothesis is independent of the dimension of the space.
13.
Biagio Ricceri 《Proceedings of the American Mathematical Society》2006,134(4):1117-1124
Here is a particular case of the main result of this paper: Let be a bounded domain, with a boundary of class , and let be two continuous functions, , with 0$">, , with n$">. If
and if the set of all global minima of the function has at least connected components, then, for each 0$"> small enough, the Neumann problem
admits at least strong solutions in .
and if the set of all global minima of the function has at least connected components, then, for each 0$"> small enough, the Neumann problem
admits at least strong solutions in .
14.
E. Ballico 《Proceedings of the American Mathematical Society》2005,133(1):1-10
Let , , be integral varieties. For any integers 0$">, , and set and . Let be the set of all linear -spaces contained in a linear -space spanned by points of , points of , ..., points of . Here we study some cases where has the expected dimension. The case was recently considered by Chiantini and Coppens and we follow their ideas. The two main results of the paper consider cases where each is a surface, more particularly:
or
or
15.
We prove the following extended version of Simons' inequality and present its applications. Let be a set and be a subset of . Let be a subset of a Hausdorff topological vector space which is invariant under infinite convex combinations. Let be a bounded function such that the functions are convex for all and whenever 0$">, and Let be a sequence in . Assume that, for every , there exists satisfying . Then
If , then the set in the above inequality can be replaced by .
If , then the set in the above inequality can be replaced by .
16.
-algebras by extensions of 
-algebras with (APD) 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).
17.
norm in some a priori estimates for non-divergence form equations in Carnot groups Donatella Danielli Nicola Garofalo Duy-Minh Nhieu 《Proceedings of the American Mathematical Society》2003,131(11):3487-3498
Let be a group of Heisenberg type with homogeneous dimension . For every we construct a non-divergence form operator and a non-trivial solution to the Dirichlet problem: in , on . This non-uniqueness result shows the impossibility of controlling the maximum of with an norm of when . Another consequence is the impossiblity of an Alexandrov-Bakelman type estimate such as
where is the dimension of the horizontal layer of the Lie algebra and is the symmetrized horizontal Hessian of .
where is the dimension of the horizontal layer of the Lie algebra and is the symmetrized horizontal Hessian of .
18.
Marc Lengfield 《Proceedings of the American Mathematical Society》2005,133(5):1401-1409
For we describe the dual spaces and Banach envelopes of the spaces for finite values of and for , the closure of the polynomials in . In addition, we determine the -Banach envelopes for the spaces in the cases and .
19.
If and are countable ordinals such that , denote by the completion of with respect to the implicitly defined norm
where the supremum is taken over all finite subsets of such that and . It is shown that the Bourgain -index of is . In particular, if \alpha =\omega^{\alpha_{1}}\cdot m_{1}+\dots+\omega^{\alpha_{n}}\cdot m_{n}$"> in Cantor normal form and is not a limit ordinal, then there exists a Banach space whose -index is .
where the supremum is taken over all finite subsets of such that and . It is shown that the Bourgain -index of is . In particular, if \alpha =\omega^{\alpha_{1}}\cdot m_{1}+\dots+\omega^{\alpha_{n}}\cdot m_{n}$"> in Cantor normal form and is not a limit ordinal, then there exists a Banach space whose -index is .
20.
Hirofumi Nakai Douglas C. Ravenel 《Proceedings of the American Mathematical Society》2003,131(5):1629-1639
There exists a -local spectrum with = . Its Adams-Novikov -term is isomorphic to
where
In this paper we determine the groups
for all 0$">. Its rank ranges from to depending on the value of .
where
In this paper we determine the groups
for all 0$">. Its rank ranges from to depending on the value of .