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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 construction of a base for the m fold tensor product of a Banach space.

Hemasinha, Rohan (1989)

International Journal of Mathematics and Mathematical Sciences

A continuum of totally incomparable hereditarily indecomposable Banach spaces

I. Gasparis (2002)

Studia Mathematica

A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.

A Hahn-Banach Theorem in Conjugate Banach Spaces.

Bernd Müller (1977)

Mathematische Zeitschrift

A local characterization of Banach lattices with order continuous norm

S. Bernau, H. Lacey (1976)

Studia Mathematica

A method for constructing orthonormal bases for non-archimedean Banach spaces of continuous functions

Ann Verdoodt (2000)

Annales mathématiques Blaise Pascal

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 $ℓ^{p}$ spaces, which generalizes the classical spaces $ℓ^{p}$ 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 New Dichotomy for Banach Spaces.

W.T. Gowers (1996)

Geometric and functional analysis

A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing $ℓ_{1}$

E. Odell (1980)

Compositio Mathematica

A note of $w c_{0}$ -basis

Sherwood Samn (1974)

Studia Mathematica

A note on Banach spaces without the approximation property

Gerald W. Johnson, Loren V. Petersen (1977)

Commentationes Mathematicae Universitatis Carolinae

A Note on Equivalent Extended Bases.

J.T. Marti (1971)

Monatshefte für Mathematik

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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