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On the Dunford-Pettis property of tensor product spaces

Ioana Ghenciu (2011)

Colloquium Mathematicae

We give sufficient conditions on Banach spaces E and F so that their projective tensor product E π F and the duals of their projective and injective tensor products do not have the Dunford-Pettis property. We prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T:E* → F** is completely continuous, then ( E ϵ F ) * does not have the DPP. We also prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T: F** → E* is completely...

On the embedding of 2-concave Orlicz spaces into L¹

Carsten Schütt (1995)

Studia Mathematica

In [K-S 1] it was shown that A v e π ( i = 1 n | x i a π ( i ) | 2 ) 1 / 2 is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we give a formula for the sequence a 1 , . . . , a n so that the above expression is equivalent to a given Orlicz norm.

On the equality between some classes of operators on Banach lattices

Belmesnaoui Aqzzouz, Aziz Elbour, Mohammed Moussa (2012)

Mathematica Bohemica

We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.

On the existence of almost greedy bases in Banach spaces

S. J. Dilworth, N. J. Kalton, Denka Kutzarova (2003)

Studia Mathematica

We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy bases begun in [3]. We show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation. We prove that if a Banach space X has a basis and contains a complemented subspace with a symmetric basis and finite cotype then X has an...

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