Chebyshev Subspaces and Convergence of Positive Linear Operators

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. r 2003 Elsevier Science (USA). All rights reserved.

Hyperinvariant subspaces and quasinilpotent operators

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

ε-weakly Chebyshev subspaces and quotient spaces

Rates of A-statistical convergence of positive linear operators

In the classical summability setting rates of summation have been introduced in several ways (see, e.g., [10], [21], [22]). The concept of statistical rates of convergence, for nonvanishing two null sequences, is studied in [13]. Unfortunately no single de...nition seems to have become the “standard” for the comparison of rates of summability transforms. The situation becomes even more uncharte...

Weighted A-Statistical Convergence for Sequences of Positive Linear Operators

We introduce the notion of weighted A-statistical convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence. Further, we give a rate of weighted A-statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our...