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Displaying similar documents to “On FU( p )-spaces and p -sequential spaces”

p -sequential like properties in function spaces

Salvador García-Ferreira, Angel Tamariz-Mascarúa (1994)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the properties of a space to be strictly WFU ( M ) or strictly SFU ( M ) , where M ω * , and we analyze them and other generalizations of p -sequentiality ( p ω * ) in Function Spaces, such as Kombarov’s weakly and strongly M -sequentiality, and Kocinac’s WFU ( M ) and SFU ( M ) -properties. We characterize these in C π ( X ) in terms of cover-properties in X ; and we prove that weak M -sequentiality is equivalent to WFU ( L ( M ) ) -property, where L ( M ) = { λ p : λ < ω 1 and p M } , in the class of spaces which are p -compact for every p M ω * ; and that C π ( X ) is a WFU ( L ( M ) ) -space iff...

A Natural Class of Sequential Banach Spaces

Jarno Talponen (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

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We introduce and study a natural class of variable exponent p spaces, which generalizes the classical spaces p and c₀. These spaces will typically not be rearrangement-invariant but instead they enjoy a good local control of some geometric properties. Some geometric examples are constructed by using these spaces.

Sequential closures of σ -subalgebras for a vector measure

Werner J. Ricker (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a locally convex space, m : Σ X be a vector measure defined on a σ -algebra Σ , and L 1 ( m ) be the associated (locally convex) space of m -integrable functions. Let Σ ( m ) denote { χ E ; E Σ } , equipped with the relative topology from L 1 ( m ) . For a subalgebra 𝒜 Σ , let 𝒜 σ denote the generated σ -algebra and 𝒜 ¯ s denote the closure of χ ( 𝒜 ) = { χ E ; E 𝒜 } in L 1 ( m ) . Sets of the form 𝒜 ¯ s arise in criteria determining separability of L 1 ( m ) ; see [6]. We consider some natural questions concerning 𝒜 ¯ s and, in particular, its relation to χ ( 𝒜 σ ) . It is shown that...

On isomorphism classes of C ( 2 [ 0 , α ] ) spaces

Elói Medina Galego (2009)

Fundamenta Mathematicae

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We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2 [ 0 , α ] , the topological sums of Cantor cubes 2 , with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C ( 2 [ 0 , α ] ) spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.

An Isomorphic Classification of C ( 2 × [ 0 , α ] ) Spaces

Elói Medina Galego (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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We present an extension of the classical isomorphic classification of the Banach spaces C([0,α]) of all real continuous functions defined on the nondenumerable intervals of ordinals [0,α]. As an application, we establish the isomorphic classification of the Banach spaces C ( 2 × [ 0 , α ] ) of all real continuous functions defined on the compact spaces 2 × [ 0 , α ] , the topological product of the Cantor cubes 2 with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. Consequently,...