Displaying similar documents to “Strong topologies on vector-valued function spaces”

Duality theory of spaces of vector-valued continuous functions

Marian Nowak, Aleksandra Rzepka (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a completely regular Hausdorff space, E a real normed space, and let C b ( X , E ) be the space of all bounded continuous E -valued functions on X . We develop the general duality theory of the space C b ( X , E ) endowed with locally solid topologies; in particular with the strict topologies β z ( X , E ) for z = σ , τ , t . As an application, we consider criteria for relative weak-star compactness in the spaces of vector measures M z ( X , E ' ) for z = σ , τ , t . It is shown that if a subset H of M z ( X , E ' ) is relatively σ ( M z ( X , E ' ) , C b ( X , E ) ) -compact, then the set conv ( S ( H ) ) is still...

Locally solid topologies on spaces of vector-valued continuous functions

Marian Nowak, Aleksandra Rzepka (2002)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a completely regular Hausdorff space and E a real normed space. We examine the general properties of locally solid topologies on the space C b ( X , E ) of all E -valued continuous and bounded functions from X into E . The mutual relationship between locally solid topologies on C b ( X , E ) and C b ( X ) ( = C b ( X , ) ) is considered. In particular, the mutual relationship between strict topologies on C b ( X ) and C b ( X , E ) is established. It is shown that the strict topology β σ ( X , E ) (respectively β τ ( X , E ) ) is the finest σ -Dini topology...

Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol (1992)

Commentationes Mathematicae Universitatis Carolinae

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An elementary construction for an abundance of vector topologies ξ on a fixed infinite dimensional vector space E such that ( E , ξ ) has not the Hahn-Banach extension property but the topological dual ( E , ξ ) ' separates points of E from zero is given.