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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 ( + ) L p ( + ) 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 n a n ( T ) = π - 1 ʃ 0 | u ( t ) v ( t ) | d t . We also provide upper and lower estimates for the α and weak 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 1 (resp. as the elements with the sequence ( x ( 4 n - 2 ) - x ( 4 n ) ) equivalent to the...

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 1 embeds as a complemented subspace of X. Pełczyński proved that every infinite-dimensional closed linear subspace of 1 contains a copy of 1 that is complemented in 1 . Later, Kadec and Pełczyński proved that every non-reflexive closed linear subspace of L 1 [ 0 , 1 ] contains a copy of 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 p , , L p , [ 0 , 1 ] , and L p , [ 0 , ) 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 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 ( + ) L p ( + ) defined by ( T f ) ( x ) v ( x ) ʃ 0 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].

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 and { F n } n = 1 are two sequences of infinite-dimensional Banach spaces then H = n = 1 E n × n = 1 F n is not B r -complete. If { E n } n = 1 and { F n } n = 1 are also reflexive spaces there is on H a separated locally convex topology , coarser than the initial one, such that H [ ] 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     obtained by the   β -numeration that are the   β -integers   β [ 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   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...