A generalization of results of R.C. James concerning absolute basis in Banach spaces

C. Bessaga; A. Pełczyński

Displaying similar documents to “A generalization of results of R.C. James concerning absolute basis in Banach spaces”

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

E. Odell (1980)

Compositio Mathematica

Similarity:

On bases and unconditional convergence of series in Banach spaces

C. Bessaga, A. Pełczyński (1958)

Studia Mathematica

Similarity:

A remark on the preceding paper of I. Singer (From a letter to R. Sikorski)

A. Pełczyński (1965)

Studia Mathematica

Similarity:

Subspaces of $L_{p}$ which embed into $l_{p}$

W. B. Johnson, E. Odell (1974)

Compositio Mathematica

Similarity:

On Banach spaces X for which $Π_{2} (ℒ_{\infty}, X) = B (ℒ_{\infty}, X)$

Ed Dubinsky, A. Pełczyński, H. Rosenthal (1972)

Studia Mathematica

Similarity:

Representing and absolutely representing systems

V. Kadets, Yu. Korobeĭnik (1992)

Studia Mathematica

Similarity:

We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.

Classification, through coordinates, of M-bases in separable Banach spaces.

Esteban Induráin (1988)

Collectanea Mathematica

Similarity:

Some remarks on symmetric basic sequences in L1

B. Maurey, G. Schechtman (1979)

Compositio Mathematica

Similarity:

Banach spaces quasi-reflexive of order one

Robert James (1977)

Studia Mathematica

Similarity:

Spreading sequences in JT

Helga Fetter, B. Gamboa de Buen (1997)

Studia Mathematica

Similarity:

We prove that a normalized non-weakly null basic sequence in the James tree space JT admits a subsequence which is equivalent to the summing basis for the James space J. Consequently, every normalized basic sequence admits a spreading subsequence which is either equivalent to the unit vector basis of $l_{2}$ or to the summing basis for J.