Displaying similar documents to “On the sublinear operators factoring through L q .”

On some structural properties of Banach function spaces and boundedness of certain integral operators

T. S. Kopaliani (2004)

Czechoslovak Mathematical Journal

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In this paper the notions of uniformly upper and uniformly lower ℓ -estimates for Banach function spaces are introduced. Further, the pair ( X , Y ) of Banach function spaces is characterized, where X and Y satisfy uniformly a lower ℓ -estimate and uniformly an upper ℓ -estimate, respectively. The integral operator from X into Y of the form K f ( x ) = ϕ ( x ) ∫ 0 x k ( x , y ) f ( y ) ψ ( y ) d y is studied, where k , ϕ , ψ are prescribed functions under some local integrability conditions, the kernel k is non-negative and is assumed to satisfy certain...

On order structure and operators in L ∞(μ)

Irina Krasikova, Miguel Martín, Javier Merí, Vladimir Mykhaylyuk, Mikhail Popov (2009)

Open Mathematics

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It is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.