Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties.     

On the density of the minimal subspaces generated by discrete linear Hamiltonian systems

This paper focuses on the density of the minimal subspaces generated by a class of discrete linear Hamiltonian systems. It is shown that the minimal subspace is densely defined if and only if the maximal subspace is an operator; that is, it is single valued. In addition, it is shown that, if the interval on which the systems are defined is bounded from below or above, then the minimal subspace is non-densely defined in any non-trivial case.     

Norm-one projections onto subspaces ofl p

Summary We give an intrinsic characterization of norm-one complemented subspaces of finite codimension in l _p (1<p< ,p 2).Work prepared under the auspices of M.P.I. (Ministero della Pubblica Istruzione) and G.N.A.F.A. of C.N.R. (Consiglio Nazionale delle Ricerche).     

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces à la W.T. Gowers' dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers' program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size ℵ₁ into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability.     

Operator-valued Fourier Haar multipliers

Criteria are given to ensure the boundedness of Fourier Haar multiplier operators from Lp([0,1],X) to Lq([0,1],Y) where the Fourier Haar multiplier sequences come not from R, as in the classical setting, but rather from the space of bounded linear operators from a Banach space X into a Banach space Y.     

The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis

In this paper we consider the Haar wavelet on weighted Herz spaces. Our weight class, whose name is Ap-dyadic local, is the one defined by the first author (2007). We shall investigate the class of Ap-dyadic weights in connection with the maximal inequalities. After obtaining the properties of weights in the first half of the present paper, we consider the Haar wavelet on weighted Herz spaces in the latter half. We shall show that the Haar wavelet basis is an unconditional basis. We also show that the Haar wavelet is not greedy except for the trivial case, that is, the Haar wavelet is greedy if and only if the Herz space under consideration is a weighted Lp space.     

多圆盘的加权Bergman空间上的不变子空间和约化子空间

本文主要研究多圆盘的加权Bergman 空间上的不变子空间和约化子空间, 给出了某些解析Toeplitz 算子的极小约化子空间的完全刻画, 以及一类解析Toeplitz 算子Tzi (1≤i≤n) 的不变子空间的Beurling 型定理.     

Some remarks on quasi-Chebyshev subspaces

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.     

The norm in C of orthogonal projections onto subspaces of polygonal functions

Let P be an orthogonal projection (in the sense of L₂) onto the subspace of polygonal functions over a certain partition of the segment [0, 1]. Z. Ciesielski has established the following estimate for the norm of this operators, as acting from C into C, valid for an arbitrary partition: P _CC 3. In this note it is proved that this estimate is final; more precisely, it is shown that .Translated from Matematicheskie Zametki, Vol. 21, No. 4, pp. 495–502, April, 1977.     

A note on norm-one projections onto subspaces of finite codimension ofl ∞

Research partially supported by Italian Ministero della Pubblica Istruzione (M.P.I.) and G.N.A.F.A. (C.N.R.)     

An infeasible-interior-point algorithm using projections onto a convex set

We present a new class of primal-dual infeasible-interior-point methods for solving linear programs. Unlike other infeasible-interior-point algorithms, the iterates generated by our methods lie in general position in the positive orthant of ² and are not restricted to some linear manifold. Our methods comprise the following features: At each step, a projection is used to recenter the variables to the domainx _i s _i . The projections are separable into two-dimensional orthogonal projections on a convex set, and thus they are seasy to implement. The use of orthogonal projections allows that a full Newton step can be taken at each iteration, even if the result violates the nonnegativity condition. We prove that a short step version of our method converges in polynomial time.Research performed while visiting the Institut für Angewandte Mathematik, University of Würzburg, D-87074 Würzburg, Germany, as a Research Fellow of the Alexander von Humboldt Foundation.     

On series by Haar system

The paper considers the series by Haar system \(\sum\limits_{n = 1}^\infty {a_n \chi _n (x)} \), satisfying the conditions \(\sum\limits_{n = 1}^\infty {a_n^2 \chi _n^2 (x)} = \infty \) and a _n χ _n (x) → 0 almost everywhere. Some theorems about correcting a function on sets of arbitrarily small measures are proved.     

On rearrangements of the double Haar system

In this paper estimates of the norm of the operator connected with the rearrangement of the double Haar system in dyadic Hardy and BMO spaces are given. Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 385–389, September, 2000.     

Fractal Haar system

The Haar system is an alternative to the classical Fourier bases, being particularly useful for the approximation of discontinuities. The article tackles the construction of a set of fractal functions close to the Haar set. The new system holds the property of constitution of bases of the Lebesgue spaces of p-integrable functions on compact intervals. Likewise, the associated fractal series of a continuous function is uniformly convergent. The case p=2 owns some peculiarities and is studied separately.