Wyniki wyszukiwania - BazTech

Ograniczanie wyników

3 Bulletin of the Polish Academy of Sciences. Mathematics

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On Some Classes of Operators on C(K, X)

Ghenciu I.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

Vol. 63, no. 3

261--274

Suppose X and Y are Banach spaces, K is a compact Hausdorff space, Σ is the σ-algebra of Borel subsets of K, C(K,X) is the Banach space of all continuous X-valued functions (with the supremum norm), and T : C(K,X) → Y is a strongly bounded operator with representing measure m : Σ → L(X,Y). We show that if T is a strongly bounded operator and T : B(K,X) → Y is its extension, then T is limited if and only if its extension T is limited, and that T∗ is completely continuous (resp. unconditionally converging) if and only if T∗ is completely continuous (resp. unconditionally converging). We prove that if K is a dispersed compact Hausdorff space and T is a strongly bounded operator, then T is limited (resp. weakly precompact, has a completely continuous adjoint, has an unconditionally converging adjoint) whenever m(A) : X → Y is limited (resp. weakly precompact, has a completely continuous adjoint, has an unconditionally converging adjoint) for each A ∈ Σ.

The embeddability of C0 in spaces of operators

Ghenciu I., Lewis P.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 3-4

239-256

Results of Emmanuele and Drewnowski are used to study the containment of c0 in the space Kw* (X*, Y), as well as the complementation of the space Kw* (X*,Y) of w*-w compact operators in the space Lw*(X*, Y) of w*-w operators from X* to Y.

Almost weakly compact operators

Ghenciu I., Lewis P.

Bulletin of the Polish Academy of Sciences. Mathematics

2006

Vol. 54, no 3-4

237-256

Dunford-Pettis type properties are studied in individual Banach spaces as well as in spaces of operators. Bibasic sequences are used to characterize Banach spaces which fail to have the Dunford-Pettis property. The question of whether a space of operators has a Dunford-Pettis property when the dual of the domain and the codomain have the respective property is studied. The notion of an almost weakly compact operator plays a consistent and important role in this study.