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1.
Let be a vector lattice of real functions on a set with , and let be a linear positive functional on . Conditions are given which imply the representation , , for some bounded charge . As an application, for any bounded charge on a field , the dual of is shown to be isometrically isomorphic to a suitable space of bounded charges on . In addition, it is proved that, under one more assumption on , is the integral with respect to a -additive bounded charge. 相似文献
3.
If and are linear operators acting between Banach spaces, we show that compactness of relative to does not in general imply that has -bound zero. We do, however, give conditions under which the above implication is valid. 相似文献
4.
We prove that if , are Banach spaces such that has nontrivial cotype and has trivial cotype, then smooth functions from into have a kind of ``harmonic" behaviour. More precisely, we show that if is a bounded open subset of and is -smooth with uniformly continuous Fréchet derivative, then is dense in . We also give a short proof of a recent result of P. Hájek. 相似文献
5.
Let be a Noetherian local ring. In this paper we supply formulae for computing the ranks of syzygy and Betti numbers of -modules of essentially monomial type. These modules are defined with respect to various -regular sequences. For example, finite length modules of monomial type over regular local rings of dimension are modules of essentially monomial type with respect to -regular sequences of length . If a module is of essentially monomial type with respect to an -regular sequence of length , then the rank of its -th syzygy is at least and its -th Betti number is at least . 相似文献
6.
Hardy's well-known Tauberian theorem for Cesàro means says that if the sequence satisfies and , then . In this paper it is shown that the hypothesis can be replaced by the weaker assumption of the statistical limit: st-lim , i.e., for every , . Similarly, the ``one-sided' Tauberian theorem of Landau and Schmidt's Tauberian theorem for the Abel method are extended by replacing and with st-lim and st-lim , respectively. The Hardy-Littlewood Tauberian theorem for Borel summability is also extended by replacing , where is a continuous parameter, with , and further replacing it by -st-lim , where is the Borel matrix method. 相似文献
7.
Let be a real Banach space, let be a closed convex subset of , and let , from into , be a pseudo-contractive mapping (i.e. for all and 1)$">. Suppose the space has a uniformly Gâteaux differentiable norm, such that every closed bounded convex subset of enjoys the Fixed Point Property for nonexpansive self-mappings. Then the path , , defined by the equation is continuous and strongly converges to a fixed point of as , provided that satisfies the weakly inward condition. 相似文献
8.
Codimension-2 fibrators are -manifolds which automatically induce approximate fibration, in the following sense: given any proper mapping from an -manifold onto a -manifold such that each point-preimage is a copy of the codimension-2 fibrator, is necessarily an approximate fibration. In this paper, we give some answers to the following question: given an -manifold which is a nontrivial connected sum, when is a codimension-2 fibrator? 相似文献
9.
On bounded domains we consider the anisotropic problems in with 1$"> and on and in with and on . Moreover, we generalize these boundary value problems to space-dimensions 2$">. Under geometric conditions on and monotonicity assumption on we prove existence and uniqueness of positive solutions. 相似文献
10.
Suppose that and are elements of a complex unital Banach algebra such that the spectrum of is -congruence-free and . We show that then is the sum of nilpotent elements. If denotes the spectral radius of , then we show that the additional assumption implies that 相似文献
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