All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 79

Showing per page

Regular methods of summability in some locally convex spaces

Costas Poulios (2009)

Commentationes Mathematicae Universitatis Carolinae

Suppose that X is a Fréchet space, 〈 a i j 〉 is a regular method of summability and ( x i ) is a bounded sequence in X . We prove that there exists a subsequence ( y i ) of ( x i ) such that: either (a) all the subsequences of ( y i ) are summable to a common limit with respect to 〈 a i j 〉 ; or (b) no subsequence of ( y i ) is summable with respect to 〈 a i j 〉 . This result generalizes the Erdös-Magidor theorem which refers to summability of bounded sequences in Banach spaces. We also show that two analogous results for some ω 1 -locally convex spaces...

Regular vector lattices of continuous functions and Korovkin-type theorems-Part I

Francesco Altomare, Mirella Cappelletti Montano (2005)

Studia Mathematica

We introduce and study a new class of locally convex vector lattices of continuous functions on a locally compact Hausdorff space, which we call regular vector lattices. We investigate some general properties of these spaces and of the subspaces of so-called generalized affine functions. Moreover, we present some Korovkin-type theorems for continuous positive linear operators; in particular, we study Korovkin subspaces for finitely defined operators, for the identity operator and for positive...

Remark on the Abstract Dirichlet Problem for Baire-One Functions

Ondřej F. K. Kalenda (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function....

Remarks on bounded sets in ( L F ) t v -spaces

Jerzy Kąkol (1995)

Commentationes Mathematicae Universitatis Carolinae

We establish the relationship between regularity of a Hausdorff ( L B ) t v -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff ( L B ) t v -space to be an ( L S ) t v -space. A factorization theorem for ( L N ) t v -spaces with property (K) is also obtained.

Currently displaying 21 – 40 of 79