The following dichotomy is established for any pair , of hereditary families of finite subsets of : Given , an infinite subset of , there exists an infinite subset of so that either , or , where denotes the set of all finite subsets of .
Given the disk algebra and an automorphism , there is associated a non-self-adjoint operator algebra called the semicrossed product of with . Buske and Peters showed that there is a one-to-one correspondence between the contractive Hilbert modules over and pairs of contractions and on satisfying . In this paper, we show that the orthogonally projective and Shilov Hilbert modules over correspond to pairs of isometries on satisfying . The problem of commutant lifting for is left open, but some related results are presented. 相似文献
We show that if is an -regular set in for which the triple integral of the Menger curvature is finite and if , then almost all of can be covered with countably many curves. We give an example to show that this is false for .
If is a foliation of an open set by smooth -dimensional surfaces, we define a class of functions , supported in , that are, roughly speaking, smooth along and of bounded variation transverse to . We investigate geometrical conditions on that imply results on pointwise Fourier inversion for these functions. We also note similar results for functions on spheres, on compact 2-dimensional manifolds, and on the 3-dimensional torus. These results are multidimensional analogues of the classical Dirichlet-Jordan test of pointwise convergence of Fourier series in one variable.
We estimate double exponential sums of the form
where is of multiplicative order modulo the prime and and are arbitrary subsets of the residue ring modulo . In the special case , our bound is nontrivial for with any fixed 0$">, while if in addition we have it is nontrivial for .
A (discrete) group is said to be maximally almost periodic if the points of are distinguished by homomorphisms into compact Hausdorff groups. A Hausdorff topology on a group is totally bounded if whenever there is such that . For purposes of this abstract, a family with a totally bounded topological group is a strongly extraresolvable family if (a) \vert G\vert$">, (b) each is dense in , and (c) distinct satisfy ; a totally bounded topological group with such a family is a strongly extraresolvable topological group.
We give two theorems, the second generalizing the first.
Theorem 1. Every infinite totally bounded group contains a dense strongly extraresolvable subgroup.
Corollary. In its largest totally bounded group topology, every infinite Abelian group is strongly extraresolvable.
Theorem 2. Let be maximally almost periodic. Then there are a subgroup of and a family such that
(i) is dense in every totally bounded group topology on ;
(ii) the family is a strongly extraresolvable family for every totally bounded group topology on such that ; and
(iii) admits a totally bounded group topology as in (ii).
Remark. In certain cases, for example when is Abelian, one must in Theorem 2 choose . In certain other cases, for example when the largest totally bounded group topology on is compact, the choice is impossible.
We prove that a variety is a discriminator variety if and only if has the Fraser-Horn property and every member of is representable as a Boolean product whose factors are directly indecomposable or trivial.
Let be a convex and dominated statistical model on the measurable space , with minimal sufficient, and let . Then , the -algebra of all permutation invariant sets belonging to the -fold product -algebra , is shown to be minimal sufficient for the corresponding model for independent observations, .
The main technical tool provided and used is a functional analogue of a theorem of Grzegorek (1982) concerning generators of .
We prove the existence of invariant projections from the Banach space of -pseudomeasures onto with for closed neutral subgroup of a locally compact group . As a main application we obtain that every closed neutral subgroup is a set of -synthesis in and in fact locally -Ditkin in . We also obtain an extension theorem concerning the Fourier algebra.
We show that the C*-algebra of a quantum sphere , 1$">, consists of continuous fields of operators in a C*-algebra , which contains the algebra of compact operators with , such that is a constant function of , where is the quotient map and is the unit circle.
We show that a family of functions meromorphic in some domain is normal, if for all the derivative omits the value and if the values that can take at the zeros of satisfy certain restrictions. As an application we obtain a new proof of a theorem of Langley which classifies the functions meromorphic in the plane such that and have no zeros.
We prove that a Banach space has the compact range property (CRP) if and only if, for any given -algebra , every absolutely summing operator from into is compact. Related results for -summing operators () are also discussed as well as operators on non-commutative -spaces and -summing operators.