Ioana Ghenciu

Complemented spaces of operators

Classical results of Kalton are used to study the complementation of the space W(X, Y) of weakly compact operators and the space K(X, Y) of compact operators in the space L(X, Y) of bounded linear operators from X to Y.

STRONGLY BOUNDED REPRESENTING MEASURES AND CONVERGENCE THEOREMS

Let K be a compact Hausdorff space, X a Banach space and C ( K, X ) the Banach space of all continuous functions f : K → X endowed with the supremum norm. In this paper we study weakly precompact operators defined on C ( K, X ).

Dunford-Pettis Properties and Spaces of Operators

J. Elton used an application of Ramsey theory to show that if X is an infinite dimensional Banach space, then c0 embeds in X, l1 embeds in X, or there is a subspace of X that fails to have the Dunford–Pettis property. Bessaga and Pelczynski showed that if c0 embeds in X ∗, then l∞ embeds in X∗. Emmanuele and John showed that if c0 embeds in K(X,Y ), then K(X,Y ) is not complemented in L(X,Y ). Classical results from Schauder basis theory are used in a study of Dunford–Pettis sets and strong Dunford–Pettis sets to extend each of the preceding theorems. The space Lw∗ (X ∗,Y ) of w∗−w continuous operators is also studied. Mathematics Department, University of Wisconsin-River Falls, River Falls, WI 54022-5001, USA e-mail: ioana.ghenciu@uwrf.edu Department of Mathematics, University of North Texas, Denton, TX 76203-1430, USA e-mail: lewis@unt.edu Received by the editors August 19, 2004. AMS subject classification: Primary: 46B20; secondary: 46B28.

Complemented Subspaces of Linear Bounded Operators

We study the complementation of the space

UNCONDITIONAL CONVERGENCE IN THE STRONG OPERATOR TOPOLOGY AND ℓ

W\left( X,Y \right)

Weak Precompactness in the Space of Vector-Valued Measures of Bounded Variation

of weakly compact operators, the space

Dunford-Pettis like properties on tensor products

K\left( X,Y \right)

The p-Gelfand–Phillips property in spaces of operators and Dunford–Pettis like sets

of compact operators, the space

The weak Gelfand-Phillips property in spaces of compact operators

U\left( X,Y \right)

On the properties (wL) and (wV)

of unconditionally converging operators, and the space