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1.
H.Mohebi Sh.Rezapour 《分析论及其应用》2003,19(3):266-272
It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces.In the final section,by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms. 相似文献
2.
Let Hn be an n-dimensional Haar subspace of
and let Hn−1 be a Haar subspace of Hn of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from Hn onto Hn−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1]. 相似文献
3.
L. P. Vlasov 《Mathematical Notes》1997,62(2):148-159
We consider finite-condimensional Chebyshev subspaces in the complex spaceC(Q), whereQ is a compact Hausdorff space, and prove analogs of some theorems established earlier for the real case by Garkavi and Brown
(in particular, we characterize such subspaces). It is shown that if the real spaceC(Q) contains finite-codimensional Chebyshev subspaces, then the same is true of the complex spaceC(Q) (with the sameQ).
Translated fromMatermaticheskie Zametki, Vol. 62, No. 2, pp. 178–191, August, 1997.
Translated by V. E. Nazaikinskii 相似文献
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Darapaneni Narayana 《Journal of Mathematical Analysis and Applications》2006,321(1):193-197
We give simple proofs of some results of Mohebi [H. Mohebi, On quasi-Chebyshev subspaces of Banach spaces, J. Approx. Theory 107 (2000) 87-95] on quasi-Chebyshev subspaces. 相似文献
7.
宋文华 《应用数学学报(英文版)》1996,12(1):64-70
SONGWENHUA(宋文华)(InstituteofMathematicalScience,DalianUniversityofTechnology,Dalian116024,China)Abstract:AcharacterizationofCh... 相似文献
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M. C. Listán-García F. Rambla-Barreno 《Numerical Functional Analysis & Optimization》2013,34(4):432-442
By means of rough convergence, we introduce two new geometric properties in Banach spaces and relate them to Chebyshev centers and some well-known classical properties, such as Kalton's M property or Garkavi's uniform rotundity in every direction. 相似文献
9.
Marie-Laurence Mazure 《Numerical Algorithms》2009,52(1):93-128
We prove that it is possible to construct Bernstein-type operators in any given Extended Chebyshev space and we show how they
are connected with blossoms. This generalises and explains a recent result by Aldas/Kounchev/Render on exponential spaces.
We also indicate why such operators automatically possess interesting shape preserving properties and why similar operators
exist in still more general frameworks, e.g., in Extended Chebyshev Piecewise spaces. We address the problem of convergence
of infinite sequences of such operators, and we do prove convergence for special instances of Müntz spaces.
相似文献
10.
G. M. Ustinov 《Mathematical Notes》1999,65(5):610-619
The property of a space to be an existence subspace is studied for subspacesE ofC(Q) such that eitherE orC(Q)/E is a Lindenstrauss space. For a Chebyshev subspaceL⊂C(Q)1 an analytic representation of the nearest element in terms of the annihilatorL
┴ is obtained.
Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 726–737, May, 1999. 相似文献
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In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev (and weakly-Chebyshev) subspaces of normed spaces with respect to a bounded set S by using elements of the dual space. 相似文献
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In this paper a new characterization of smooth normed linear spaces is discussed using the notion of proximal points of a pair of convex sets. It is proved that a normed linear space is smooth if and only if for each pair of convex sets, points which are mutually nearest to each other from the respective sets are proximal. 相似文献
13.
A. DowJ. Vermeer 《Topology and its Applications》1993,50(3):263-282
A characterization of compact subspaces of extremally disconnected spaces is given which is similar to Gleason's characterization that the extremally disconnected spaces are projective for the class of compact spaces. An equivalence is established between the questions of whether every basically disconnected space is embeddable into an extremally disconnected space and the Borel lifting problems for the category algebras of generalized Cantor cubes. We study an inductive method of strengthening the product topology on the Cantor cubes to extremally disconnected topologies and use this to establish, from CH, that every compact F-space of weight c+ embeds into an extremally disconnected space. 相似文献
14.
Marie-Laurence Mazure 《Advances in Computational Mathematics》2001,14(2):129-156
For polynomial splines as well as for Chebyshev splines, it is known that total positivity of the connection matrices is sufficient to obtain B-spline bases. In this paper we give a necessary and sufficient condition for the existence of B-bases (or, equivalently, of blossoms) for splines with connection matrices and with sections in different four-dimensional extended Chebyshev spaces. 相似文献
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Alex Chigogidze 《Proceedings of the American Mathematical Society》2001,129(10):2959-2963
We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.
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In this note we see another circumstance where Chebyshev polynomials play a significant role. In particular, we present some new extended Chebyshev spaces that arise in the asymptotic stability of the zero solution of first order linear delay differential equations with m commensurate delays where aj,j=0,…,m, are constants and τ>0 is constant. 相似文献
18.
Heinz H. Bauschke Xianfu Wang Jane Ye Xiaoming Yuan 《Journal of Approximation Theory》2009,159(1):3-25
A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed set is Chebyshev if and only if the set is convex. In this paper, from the more general perspective of Bregman distances, we show that if every point in the space has a unique nearest point in a closed set, then the set is convex. We provide two approaches: one is by nonsmooth analysis; the other by maximal monotone operator theory. Subdifferentiability properties of Bregman nearest distance functions are also given. 相似文献
19.
The use of extended Chebyshev spaces in geometric design is motivated by the interesting shape parameters they provide. Unfortunately
the algorithms such spaces lead to are generally complicated because the blossoms themselves are complicated. In order to
make up for this inconvenience, we here investigate particular extended Chebyshev spaces, containing the constants and power
functions whose exponents are consecutive positive integers. We show that these spaces lead to simple algorithms due to the
fact that the blossoms are polynomial functions. Furthermore, we also describe an elegant dimension elevation algorithm which
makes it possible to return to polynomial spaces and therefore to use all the classical algorithms for polynomials.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
When G is a finite dimensional Haar subspace of C(X,Rk), the vector-valued continuous functions (including complex-valued functions when k is 2) from a finite set X to Euclidean k-dimensional space, it is well-known that at any function f in C(X,Rk) the best approximation operator satisfies the strong unicity condition of order 2 and a Lipschitz (Hőlder) condition of order . This note shows that in fact the best approximation operator satisfies the usual Lipschitz condition of order 1. 相似文献