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 .
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 .
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 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 .
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 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.
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 .
Let be a generalized frame in a separable Hilbert space indexed by a measure space , and assume its analysing operator is surjective. It is shown that is essentially discrete; that is, the corresponding index measure space can be decomposed into atoms such that is isometrically isomorphic to the weighted space of all sequences of complex numbers with , where This provides a new proof for the redundancy of the windowed Fourier transform as well as any wavelet family in .
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.
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.
for every and every with .
where each is the -weakly closed Alg -submodule determined by an order homomorphism from into itself.
In this framework, a central quantity introduced by Grekos is the function defined as the following maximum (taken over all bases of exact order ):
In this paper, we introduce a new and simple method for the study of this function. We obtain a new estimate from above for which improves drastically and in any case on all previously known estimates. Our estimate, namely , cannot be too far from the truth since verifies . However, it is certainly not always optimal since . Our last result shows that is in fact a strictly increasing sequence.
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.