Complex Unconditional Metric Approximation Property for $C_{Λ}()$ spaces

Daniel Li

Displaying similar documents to “Complex Unconditional Metric Approximation Property for $C_{Λ} ()$ spaces”

Two-sided estimates of the approximation numbers of certain Volterra integral operators

D. Edmunds, W. Evans, D. Harris (1997)

Studia Mathematica

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We consider the Volterra integral operator $T : L^{p} (ℝ^{+}) \to L^{p} (ℝ^{+})$ defined by $(T f) (x) = v (x) ʃ_{0}^{x} u (t) f (t) d t$ . Under suitable conditions on u and v, upper and lower estimates for the approximation numbers $a_{n} (T)$ of T are established when 1 < p < ∞. When p = 2 these yield $l i m_{n \to \infty} n a_{n} (T) = π^{- 1} ʃ_{0}^{\infty} | u (t) v (t) | d t$ . We also provide upper and lower estimates for the $ℓ^{α}$ and weak $ℓ^{α}$ norms of (an(T)) when 1 < α < ∞.

Characterizations of elements of a double dual Banach space and their canonical reproductions

Vassiliki Farmaki (1993)

Studia Mathematica

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For every element x** in the double dual of a separable Banach space X there exists the sequence $(x^{(2 n)})$ of the canonical reproductions of x** in the even-order duals of X. In this paper we prove that every such sequence defines a spreading model for X. Using this result we characterize the elements of X**╲ X which belong to the class $B_{1} (X) ╲ B_{1 / 2} (X)$ (resp. to the class $B_{1 / 4} (X)$ ) as the elements with the sequence $(x^{(2 n)})$ equivalent to the usual basis of $ℓ^{1}$ (resp. as the elements with the sequence $(x^{(4 n - 2)} - x^{(4 n)})$ equivalent to the...

The Compact Approximation Property does not imply the Approximation Property

George Willis (1992)

Studia Mathematica

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It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.

Mapping Properties of $c_{0}$

Paul Lewis (1999)

Colloquium Mathematicae

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Bessaga and Pełczyński showed that if $c_{0}$ embeds in the dual $X^{*}$ of a Banach space X, then $ℓ^{1}$ embeds as a complemented subspace of X. Pełczyński proved that every infinite-dimensional closed linear subspace of $ℓ^{1}$ contains a copy of $ℓ^{1}$ that is complemented in $ℓ^{1}$ . Later, Kadec and Pełczyński proved that every non-reflexive closed linear subspace of $L^{1} [0, 1]$ contains a copy of $ℓ^{1}$ that is complemented in $L^{1} [0, 1]$ . In this note a traditional sliding hump argument is used to establish a simple mapping property of...

Isomorphism of certain weak $L^{p}$ spaces

Denny Leung (1993)

Studia Mathematica

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It is shown that the weak $L^{p}$ spaces $ℓ^{p, \infty}, L^{p, \infty} [0, 1]$ , and $L^{p, \infty} [0, \infty)$ are isomorphic as Banach spaces.

L-summands in their biduals have Pełczyński's property (V*)

Hermann Pfitzner (1993)

Studia Mathematica

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Banach spaces which are L-summands in their biduals - for example $l^{1}$ , the predual of any von Neumann algebra, or the dual of the disc algebra - have Pełczyński’s property (V*), which means that, roughly speaking, the space in question is either reflexive or is weakly sequentially complete and contains many complemented copies of $l^{1}$ .

Two-sided estimates for the approximation numbers of Hardy-type operators in $L^{\infty}$ and L¹

W. Evans, D. Harris, J. Lang (1998)

Studia Mathematica

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In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator $T : L^{p} (ℝ^{+}) \to L^{p} (ℝ^{+})$ defined by $(T f) (x) ≔ v (x) ʃ_{0}^{\infty} u (t) f (t) d t$ when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].

An approximation problem in $L^{p} ([0, 2 π])$ , 2 < p < ∞

Daniel Oberlin (1981)

Studia Mathematica

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On $B_{r}$ -completeness

Manuel Valdivia (1975)

Annales de l'institut Fourier

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In this paper it is proved that if ${E_{n}}_{n = 1}^{\infty}$ and ${F_{n}}_{n = 1}^{\infty}$ are two sequences of infinite-dimensional Banach spaces then $H = (\oplus_{n = 1}^{\infty} E_{n}) \times \prod_{n = 1}^{\infty} F_{n}$ is not $B_{r}$ -complete. If ${E_{n}}_{n = 1}^{\infty}$ and ${F_{n}}_{n = 1}^{\infty}$ are also reflexive spaces there is on $H$ a separated locally convex topology $ℱ$ , coarser than the initial one, such that $H [ℱ]$ is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on $B_{r}$ -completeness and bornological spaces.

On the complemented subspaces of the Schreier spaces

I. Gasparis, D. Leung (2000)

Studia Mathematica

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It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space $X^{ξ}$ generated by subsequences $(e_{l_{n}}^{ξ})$ and $(e_{m_{n}}^{ξ})$ , respectively, of the natural Schauder basis $(e_{n}^{ξ})$ of $X^{ξ}$ are isomorphic if and only if $(e_{l_{n}}^{ξ})$ and $(e_{m_{n}}^{ξ})$ are equivalent. Further, $X^{ξ}$ admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of $(e_{n}^{ξ})$ . It is also shown that there exists a complemented subspace spanned by a block basis of $(e_{n}^{ξ})$ , which is not isomorphic to a subspace generated by a subsequence of $(e_{n}^{ζ})$ ,...

Geometric study of the beta-integers for a Perron number and mathematical quasicrystals

Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2004)

Journal de Théorie des Nombres de Bordeaux

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We investigate in a geometrical way the point sets of $ℝ$ obtained by the $β$ -numeration that are the $β$ -integers $ℤ_{β} \subset ℤ [β]$ where $β$ is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the $β$ -numeration, allowing to lift up the $β$ -integers to some points of the lattice $ℤ^{m}$ ( $m =$ degree of $β$ ) lying about the dominant eigenspace of the companion matrix of $β$ . When $β$ is in particular a Pisot number, this framework gives another proof of the fact...

Displaying similar documents to “Complex Unconditional Metric Approximation Property for C Λ ( ) spaces”

Displaying similar documents to “Complex Unconditional Metric Approximation Property for $C_{Λ} ()$ spaces”