Displaying similar documents to “Lower bound and upper bound of operators on block weighted sequence spaces”

Ultrafilter-limit points in metric dynamical systems

Salvador García-Ferreira, Manuel Sanchis (2007)

Commentationes Mathematicae Universitatis Carolinae

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Given a free ultrafilter p on ℕ and a space X , we say that x ∈ X is the p -limit point of a sequence ( x n ) n ∈ ℕ in X (in symbols, x = p - lim n → ∞ x n ) if for every neighborhood V of x , { n ∈ ℕ : x n ∈ V } ∈ p . By using p -limit points from a suitable metric space, we characterize the selective ultrafilters on ℕ and the P -points of ℕ * = β ( ℕ ) ∖ ℕ . In this paper, we only consider dynamical systems ( X , f ) , where X is a compact metric space. For a free ultrafilter p on ℕ * , the function f p : X → X is defined by f p ( x ) = p - lim n → ∞ f n ( x ) for each x ∈ X . These functions are not continuous in general....

Embedding c 0 in bvca ( Σ , X )

Juan Carlos Ferrando, L. M. Sánchez Ruiz (2007)

Czechoslovak Mathematical Journal

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If ( Ω , Σ ) is a measurable space and X a Banach space, we provide sufficient conditions on Σ and X in order to guarantee that b v c a ( Σ , X ) , the Banach space of all X -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of c 0 if and only if X does.

On the composition of the integral and derivative operators of functional order

Silvia I. Hartzstein, Beatriz E. Viviani (2003)

Commentationes Mathematicae Universitatis Carolinae

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The Integral, I φ , and Derivative, D φ , operators of order φ , with φ a function of positive lower type and upper type less than 1 , were defined in [HV2] in the setting of spaces of homogeneous-type. These definitions generalize those of the fractional integral and derivative operators of order α , where φ ( t ) = t α , given in [GSV]. In this work we show that the composition T φ = D φ ∘ I φ is a singular integral operator. This result in addition with the results obtained in [HV2] of boundedness of I φ and D φ or the...

Indiscernibles and dimensional compactness

C. Ward Henson, Pavol Zlatoš (1996)

Commentationes Mathematicae Universitatis Carolinae

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This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set u S ⊆ G in a biequivalence vector space 〈 W , M , G 〉 , such that x - y ∉ M for distinct x , y ∈ u , contains an infinite independent subset. Consequently, a class X ⊆ G is dimensionally compact iff the π -equivalence ≐ M is compact on X . This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author.