Displaying similar documents to “A note on uniformly dominated sets of summing operators.”

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.

Dual convergences of iteration processes for nonexpansive mappings in Banach spaces

Jong Soo Jung, Daya Ram Sahu (2003)

Czechoslovak Mathematical Journal

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In this paper we establish a dual weak convergence theorem for the Ishikawa iteration process for nonexpansive mappings in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, and then apply this result to study the problem of the weak convergence of the iteration process.

On infinite dimensional uniform smoothness of Banach spaces

Stanisław Prus (1999)

Commentationes Mathematicae Universitatis Carolinae

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An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some l p -type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.