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1
Content available remote

The dual of the James tree space is asymptotically uniformly convex

100%
Girardi M.
Studia Mathematica
|
2001
|
tom 147
|
nr 2
119-130
EN
The dual of the James tree space is asymptotically uniformly convex.
2
Content available remote

Banach spaces which admit a norm with the uniform Kadec-Klee property

51%
J. Dilworth S., Girardi M., Kutzarova D.
Studia Mathematica
|
1994-1995
|
tom 112
|
nr 3
267-277
EN
Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space $L_2(Ӿ)$ if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.
3
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From weak to strong types of $L^{1}_{E}$-convergence by the Bocce criterion

51%
J. Balder E., Girardi M., Jalby V.
Studia Mathematica
|
1994
|
tom 111
|
nr 3
241-262
EN
Necessary and sufficient oscillation conditions are given for a weakly convergent sequence (resp. relatively weakly compact set) in the Bochner-Lebesgue space $ℒ^{1}_{E}$ to be norm convergent (resp. relatively norm compact), thus extending the known results for $ℒ^{1}_{ℝ}$. Similarly, necessary and sufficient oscillation conditions are given to pass from weak to limited (and also to Pettis-norm) convergence in $ℒ^{1}_{E}$. It is shown that tightness is a necessary and sufficient condition to pass from limited to strong convergence. Other implications between several modes of convergence in $ℒ^{1}_{E}$ are also studied.
4
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Geometry of Banach spaces and biorthogonal systems

51%
Dilworth S. J., Girardi M., Johnson W. B.
Studia Mathematica
|
2000
|
tom 140
|
nr 3
243-271
EN
A separable Banach space X contains $ℓ_1$ isomorphically if and only if X has a bounded fundamental total $wc_{0}*$-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total $wc_{0}*$-biorthogonal system.
5
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Weak vs. norm compactness in $L_{1}$: the Bocce criterion

38%
Girardi M.
Studia Mathematica
|
1991
|
tom 98
|
nr 1
95-97
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