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It is shown that the dual of the space Cp(I) of all real-valued continuous functions on the closed unit interval with the pointwise topology, when equipped with the Mackey topology, is a non K-analytic but weakly analytic locally convex space.

A new type of convergence (called uniformly pointwise convergence) for a sequence of scalar valued functions is introduced. If (fn) is a uniformly bounded sequence of functions in l∞(Γ), it is proved that:

(i) (fn) converges uniformly pointwise on Γ to some function f if, and only if, every subsequence of (fn) is Cesaro summable in l∞(Γ); and

(ii) there exists a subsequence (f′n) of (fn) such that either (f′n) converges uniformly pointwise on Γ to some f or no subsequence of (f′n) is Cesaro-summable in l∞(Γ).

Applications of the above results in Banach space theory are given.

A natural and welcomed decomposition theorem for elements in the positive cone of the tensor product of Archimedean vector lattices leads to substantial simplifications in the theory of tensor products of Archimedean vector lattices.

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A WEAKLY ANALYTIC LOCALLY CONVEX SPACE WHICH IS NOT K-ANALYTIC

On Cesaro summable sequences of continuous functions

A decomposition theorem in tensor products of Archimedean vector lattices

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103 results in 46Axx

A WEAKLY ANALYTIC LOCALLY CONVEX SPACE WHICH IS NOT K-ANALYTIC

On Cesaro summable sequences of continuous functions

A decomposition theorem in tensor products of Archimedean vector lattices