More (\ell_r) saturated (\mathcal{L}_\infty) spaces
We present some new examples of separable (\mathcal_\infty) spaces which are (\ell_r) saturated for some (1 < r < \infty).
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arXiv subjects
I. Gasparis
Publications and source records attributed to I. Gasparis.
Weakly null sequences in the Banach space C(K)
The hierarchy of the block bases of transfinite normalized averages of a normalized Schauder basic sequence is introduced and a criterion is given for a normalized weakly null sequence in C(K), the Banach space of scalar valued functions continuous on the compact metric space K, to admit a block basis of normalized averages equivalent to the unit vector basis of c_0, the Banach space of null scalar sequences. As an application of this criterion, it is shown that every normalized weakly null sequence in C(K), for countable K, admits a block basis of normalized averages equivalent to the unit vector basis of c_0.
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Unconditional structures of weakly null sequences
The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of c, the Banach space of null sequences under the supremum norm, or there exists a subsequence which is boundedly convexly complete. This result generalizes J. Elton's dichotomy on weakly null sequences.
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On the complemented subspaces of the Schreier spaces
It is shown that the Schreier space X admits a set of continuum cardinality whose elements are mutually incomparable complemented subspaces spanned by subsequences of the natural Schauder basis of X.
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