Operators with an integral reprsentation
Copyright policy )Operators with an integral reprsentation
We introduce a fairly large class of bounded linear operators between Banach spaces which admit an integral representation. It turns out that an operator belongs to this class if and only if it factors through a C ( K ) C(K) space. As an application, we characterize Banach spaces containing no copy of c 0 c_0 , Banach spaces containing no complemented copy of ℓ 1 \ell _1 , Grothendieck spaces, and L ∞ \mathscr L_{\infty } -spaces. We also study C ( K ) C(K) -factorization and extension properties of absolutely continuous operators, giving a partial answer to a question raised in 1985 by H. Jarchow and U. Matter.
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Operator ideals, Isomorphic theory (including renorming) of Banach spaces, Banach space, Operator, Summing operators., factorization through \(C(K)\) spaces, absolutely continuous operators, integral representation, Spaces of operators; tensor products; approximation properties, extendible operators, \(\infty\)-integral operators
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Operator ideals, Isomorphic theory (including renorming) of Banach spaces, Banach space, Operator, Summing operators., factorization through \(C(K)\) spaces, absolutely continuous operators, integral representation, Spaces of operators; tensor products; approximation properties, extendible operators, \(\infty\)-integral operators
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