Convergence of monotone nets in ordered topological vector spaces

Charles McArthur

Displaying similar documents to “Convergence of monotone nets in ordered topological vector spaces”

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.

Symmetric bases of locally convex spaces

D. Garling (1968)

Studia Mathematica

Similarity:

Normalized bases in topological vector spaces

Kamthan, P.K. (1979)

Portugaliae mathematica

Similarity:

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

E. Odell (1980)

Compositio Mathematica

Similarity:

Unconditional and normalised bases

N. Kalton (1970)

Studia Mathematica

Similarity:

On bases and unconditional convergence of series in Banach spaces

C. Bessaga, A. Pełczyński (1958)

Studia Mathematica

Similarity:

On unconditional bases in certain Banach function spaces

J. Shirey, R. Zink (1970)

Studia Mathematica

Similarity:

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

Esteban Induráin (1988)

Collectanea Mathematica

Similarity:

Existence of some special bases in Banach spaces

P. Wojtaszczyk (1973)

Studia Mathematica

Similarity:

Uniqueness of unconditional bases of $c_{0} (l_{p})$ , 0 < p < 1

C. Leránoz (1992)

Studia Mathematica

Similarity:

We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of $c_{0} (l_{p})$ must be equivalent to a permutation of a subset of the canonical unit vector basis of $c_{0} (l_{p})$ . In particular, $c_{0} (l_{p})$ has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for $c_{0} (l ₁)$ .