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1.
Pietro Aiena 《Journal of Mathematical Analysis and Applications》2008,342(2):830-837
This note is a continuation of a previous article [P. Aiena, M.T. Biondi, Property (w) and perturbations, J. Math. Anal. Appl. 336 (2007) 683-692] concerning the stability of property (w), a variant of Weyl's theorem, for a bounded operator T acting on a Banach space, under finite-dimensional perturbations K commuting with T. A counterexample shows that property (w) in general is not preserved under finite-dimensional perturbations commuting with T, also under the assumption that T is a-isoloid. 相似文献
2.
Michael Gnewuch 《Journal of Complexity》2012,28(1):2-17
We extend the notion of L2-B-discrepancy introduced in [E. Novak, H. Wo?niakowski, L2 discrepancy and multivariate integration, in: W.W.L. Chen, W.T. Gowers, H. Halberstam, W.M. Schmidt, and R.C. Vaughan (Eds.), Analytic Number Theory. Essays in Honour of Klaus Roth, Cambridge University Press, Cambridge, 2009, pp. 359-388] to what we shall call weighted geometric L2-discrepancy. This extension enables us to consider weights in order to moderate the importance of different groups of variables, as well as to consider volume measures different from the Lebesgue measure and classes of test sets different from measurable subsets of Euclidean spaces.We relate the weighted geometric L2-discrepancy to numerical integration defined over weighted reproducing kernel Hilbert spaces and settle in this way an open problem posed by Novak and Wo?niakowski.Furthermore, we prove an upper bound for the numerical integration error for cubature formulas that use admissible sample points. The set of admissible sample points may actually be a subset of the integration domain of measure zero. We illustrate that particularly in infinite-dimensional numerical integration it is crucial to distinguish between the whole integration domain and the set of those sample points that actually can be used by the algorithms. 相似文献
3.
F. Rambla 《Journal of Mathematical Analysis and Applications》2006,317(2):659-667
We prove that if the one-point compactification of a locally compact, noncompact Hausdorff space L is the topological space called pseudoarc, then C0(L,C) is almost transitive. We also obtain two necessary conditions on a metrizable locally compact Hausdorff space L for C0(L) being almost transitive. 相似文献
4.
Mixed generalized dimensions of self-similar measures 总被引:1,自引:0,他引:1
L. Olsen 《Journal of Mathematical Analysis and Applications》2005,306(2):516-539
5.
When A∈B(H) and B∈B(K) are given, we denote by MC the operator acting on the infinite-dimensional separable Hilbert space H⊕K of the form . In this paper, it is shown that there exists some operator C∈B(K,H) such that MC is upper semi-Fredholm and ind(MC)?0 if and only if there exists some left invertible operator C∈B(K,H) such that MC is upper semi-Fredholm and ind(MC)?0. A necessary and sufficient condition for MC to be upper semi-Fredholm and ind(MC)?0 for some C∈Inv(K,H) is given, where Inv(K,H) denotes the set of all the invertible operators of B(K,H). In addition, we give a necessary and sufficient condition for MC to be upper semi-Fredholm and ind(MC)?0 for all C∈Inv(K,H). 相似文献
6.
Lim's theorems for multivalued mappings in CAT(0) spaces 总被引:1,自引:0,他引:1
Let X be a complete CAT(0) space. We prove that, if E is a nonempty bounded closed convex subset of X and a nonexpansive mapping satisfying the weakly inward condition, i.e., there exists p∈E such that ∀x∈E, ∀α∈[0,1], then T has a fixed point. In Banach spaces, this is a result of Lim [On asymptotic centers and fixed points of nonexpansive mappings, Canad. J. Math. 32 (1980) 421-430]. The related result for unbounded R-trees is given. 相似文献
7.
Let m be a positive integer and let G be a graph. We consider the question: can the edge set E(G) of G be expressed as the union of a set M of matchings of G each of which has size exactly m? If this happens, we say that G is [m]-coverable and we call M an [m]-covering of G. It is interesting to consider minimum[m]-coverings, i.e. [m]-coverings containing as few matchings as possible. Such [m]-coverings will be called excessive[m]-factorizations. The number of matchings in an excessive [m]-factorization is a graph parameter which will be called the excessive[m]-index and denoted by . In this paper we begin the study of this new parameter as well as of a number of other related graph parameters. 相似文献
8.
Ferenc Móricz 《Journal of Mathematical Analysis and Applications》2008,342(2):1246-1249
We study the smoothness property of a function f with absolutely convergent Fourier series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs to one of the Zygmund classes Λ∗(α) and λ∗(α) for some 0<α?2. This paper is a natural supplement to our earlier one [F. Móricz, Absolutely convergent Fourier series and function classes, J. Math. Anal. Appl. 324 (2) (2006) 1168-1177] under the same title, and we keep its notations. 相似文献
9.
Kinkar Ch. Das 《Discrete Applied Mathematics》2010,158(11):1181-2037
The recently introduced atom-bond connectivity (ABC) index has been applied up until now to study the stability of alkanes and the strain energy of cycloalkanes. Furtula et al. (2009) [3] obtained extremal ABC values for chemical trees, and also, it has been shown that the star K1,n−1, has the maximal ABC value of trees. In this paper, we present the lower and upper bounds on ABC index of graphs and trees, and characterize graphs for which these bounds are best possible. 相似文献
10.
A.G. Smirnov 《Journal of Mathematical Analysis and Applications》2009,351(1):57-69
In [A.G. Smirnov, Fourier transformation of Sato's hyperfunctions, Adv. Math. 196 (2005) 310-345] the author introduced a new generalized function space U(Rk) which can be naturally interpreted as the Fourier transform of the space of Sato's hyperfunctions on Rk. It was shown that all Gelfand-Shilov spaces (α>1) of analytic functionals are canonically embedded in U(Rk). While the usual definition of support of a generalized function is inapplicable to elements of and U(Rk), their localization properties can be consistently described using the concept of carrier cone introduced by Soloviev [M.A. Soloviev, Towards a generalized distribution formalism for gauge quantum fields, Lett. Math. Phys. 33 (1995) 49-59; M.A. Soloviev, An extension of distribution theory and of the Paley-Wiener-Schwartz theorem related to quantum gauge theory, Comm. Math. Phys. 184 (1997) 579-596]. In this paper, the relation between carrier cones of elements of and U(Rk) is studied. It is proved that an analytic functional is carried by a cone K⊂Rk if and only if its canonical image in U(Rk) is carried by K. 相似文献
11.
Jeffrey L. Boersema 《Journal of Functional Analysis》2006,235(2):702-718
We prove that the united K-theory functor is a surjective functor from the category of real simple separable purely infinite C∗-algebras to the category of countable acyclic CRT-modules. As a consequence, we show that every complex Kirchberg algebra satisfying the universal coefficient theorem is the complexification of a real C∗-algebra. 相似文献
12.
Ferenc Móricz 《Journal of Mathematical Analysis and Applications》2006,324(2):1168-1177
We study the smoothness property of a function f with absolutely convergent Fourier series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs either to one of the Lipschitz classes Lip(α) and lip(α) for some 0<α?1, or to one of the Zygmund classes Λ∗(1) and λ∗(1). Our theorems generalize some of those by Boas [R.P. Boas Jr., Fourier series with positive coefficients, J. Math. Anal. Appl. 17 (1967) 463-483] and one by Németh [J. Németh, Fourier series with positive coefficients and generalized Lipschitz classes, Acta Sci. Math. (Szeged) 54 (1990) 291-304]. We also prove a localized version of a theorem by Paley [R.E.A.C. Paley, On Fourier series with positive coefficients, J. London Math. Soc. 7 (1932) 205-208] on the existence and continuity of the derivative of f. 相似文献
13.
Kit C. Chan 《Journal of Mathematical Analysis and Applications》2011,375(1):139-148
Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong operator topology, and along which every operator has the exact same dense Gδ set of hypercyclic vectors. In the present work, we show that the conjugate set of any hypercyclic operator on a separable, infinite dimensional Banach space always contains a path of operators which is dense with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense Gδ set. As a corollary, the hypercyclic operators on such a Banach space form a connected subset of the operator algebra with the strong operator topology. 相似文献
14.
Anita Pasotti 《Discrete Mathematics》2010,310(22):3080-3087
J.A. Gallian has proved [J.A. Gallian, Labeling prisms and prism related graphs, Congr. Numer. 59 (1987) 89-100] that every cubic graph M2k obtainable from a 2k-cycle by adding its k diameters (the so-called Moebius Ladder of order 2k) is graceful. Here, in the case of k even, we propose a new graceful labeling that besides being simpler than Gallian’s one is able to give, at the same time, a graceful labeling of the prism of order 2k. Most importantly in the case of k odd, namely in the bipartite case, we prove that M2k also admits an α-labeling. This implies that there exists a cyclic decomposition of the complete graph K6kt+1 into copies of M2k for every pair of positive integers k and t with k odd.In some cases we are able to give such decompositions also when k is even. Apart from the case of t=1 that is an obvious consequence of the gracefulness of M2k, this happens, for instance, when k≡2 (mod 4) and 6kt+1 is a prime. 相似文献
15.
Rafael Espínola Adrian Petru?el 《Journal of Mathematical Analysis and Applications》2005,309(2):420-432
The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued aα-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petru?el, and Sînt?m?rian [I.A. Rus, A. Petru?el, A. Sînt?m?rian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959]. 相似文献
16.
Juan Carlos Ferrando 《Journal of Mathematical Analysis and Applications》2011,380(1):323-326
If (Σ,X) is a measurable space and X a Banach space we investigate the X-inheritance of copies of ?∞ in certain subspaces Δ(Σ,X) of bvca(Σ,X), the Banach space of all X-valued countable additive measures of bounded variation equipped with the variation norm. Among the consequences of our main theorem we get a theorem of J. Mendoza on the X-inheritance of copies of ?∞ in the Bochner space L1(μ,X) and other of the author on the X-inheritance of copies of ?∞ in bvca(Σ,X). 相似文献
17.
Andreas Löhne 《Journal of Mathematical Analysis and Applications》2006,319(2):617-634
In this paper we introduce a convergence concept for closed convex subsets of a finite-dimensional normed vector space. This convergence is called C-convergence. It is defined by appropriate notions of upper and lower limits. We compare this convergence with the well-known Painlevé-Kuratowski convergence and with scalar convergence. In fact, we show that a sequence (An)n∈NC-converges to A if and only if the corresponding support functions converge pointwise, except at relative boundary points of the domain of the support function of A, to the support function of A. 相似文献
18.
By a ball-covering B of a Banach space X, we mean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere SX of X; and X is said to have the ball-covering property (BCP) provided it admits a ball-covering by countably many balls. In this note we give a natural example showing that the ball-covering property of a Banach space is not inherited by its subspaces; and we present a sharp quantitative version of the recent Fonf and Zanco renorming result saying that if the dual X∗ of X is w∗ separable, then for every ε>0 there exist a (1+ε)-equivalent norm on X, and an R>0 such that in this new norm SX admits a ball-covering by countably many balls of radius R. Namely, we show that R=R(ε) can be taken arbitrarily close to (1+ε)/ε, and that for X=?1[0,1] the corresponding R cannot be equal to 1/ε. This gives the sharp order of magnitude for R(ε) as ε→0. 相似文献
19.
Regina Rotman 《Topology》2007,46(4):343-356
In this paper we will estimate the smallest length of a minimal geodesic net on an arbitrary closed Riemannian manifold Mn in terms of the diameter of this manifold and its dimension. Minimal geodesic nets are critical points of the length functional on the space of immersed graphs into a Riemannian manifold. We prove that there exists a minimal geodesic net that consists of m geodesics connecting two points p,q∈Mn of total length ≤md, where m∈{2,…,(n+1)} and d is the diameter of Mn. We also show that there exists a minimal geodesic net with at most n+1 vertices and geodesic segments of total length .These results significantly improve one of the results of [A. Nabutovsky, R. Rotman, The minimal length of a closed geodesic net on a Riemannian manifold with a nontrivial second homology group, Geom. Dedicata 113 (2005) 234-254] as well as most of the results of [A. Nabutovsky, R. Rotman, Volume, diameter and the minimal mass of a stationary 1-cycle, Geom. Funct. Anal. 14 (4) (2004) 748-790]. 相似文献
20.
Li Hui Peng 《Journal of Mathematical Analysis and Applications》2007,325(2):987-1002
Let X be a Banach space and Z a nonempty closed subset of X. Let be an upper semicontinuous function bounded from above. This paper is concerned with the perturbed optimization problem supz∈Z{J(z)+‖x−z‖}, which is denoted by (x,J)-sup. We shall prove in the present paper that if Z is a closed boundedly relatively weakly compact nonempty subset, then the set of all x∈X for which the problem (x,J)-sup has a solution is a dense Gδ-subset of X. In the case when X is uniformly convex and J is bounded, we will show that the set of all points x in X for which there does not exist z0∈Z such that J(z0)+‖x−z0‖=supz∈Z{J(z)+‖x−z‖} is a σ-porous subset of X and the set of all points x∈X?Z0 such that there exists a maximizing sequence of the problem (x,J)-sup which has no convergent subsequence is a σ-porous subset of X?Z0, where Z0 denotes the set of all z∈Z such that z is in the solution set of (z,J)-sup. 相似文献