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

• Autorzy: Ghenciu I.

Identyfikatory

DOI

10.4064/ba7997-1-2016

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

limited operators; weakly precompact operators; spaces of continuous functions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: Vol. 63, no. 3
• Strony: 261--274
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Ghenciu I.

• Department of Mathematics, University of Wisconsin–River Falls, River Falls, WI 54022-5001, U.S.A.

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