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A conditional quasi-greedy basis of l₁

S. J. Dilworth, David Mitra (2001)

Studia Mathematica

We show that the Lindenstrauss basic sequence in l₁ may be used to construct a conditional quasi-greedy basis of l₁, thus answering a question of Wojtaszczyk. We further show that the sequence of coefficient functionals for this basis is not quasi-greedy.

A Natural Class of Sequential Banach Spaces

Jarno Talponen (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

We introduce and study a natural class of variable exponent p spaces, which generalizes the classical spaces p and c₀. These spaces will typically not be rearrangement-invariant but instead they enjoy a good local control of some geometric properties. Some geometric examples are constructed by using these spaces.

A note on fusion Banach frames

S. K. Kaushik, Varinder Kumar (2010)

Archivum Mathematicum

For a fusion Banach frame ( { G n , v n } , S ) for a Banach space E , if ( { v n * ( E * ) , v n * } , T ) is a fusion Banach frame for E * , then ( { G n , v n } , S ; { v n * ( E * ) , v n * } , T ) is called a fusion bi-Banach frame for E . It is proved that if E has an atomic decomposition, then E also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.

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