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Displaying 401 – 420 of 478

Uniqueness of (...) Bases and Isometries of Banach Spaces.

Y. Gordon, R. Loewy (1979)

Mathematische Annalen

Uniqueness of some unconditional bases II

J. Lindenstrauss (1980/1981)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Uniqueness of unconditional bases in $c_{0}$ -products

P. Casazza, N. Kalton (1999)

Studia Mathematica

We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does $c_{0} (X)$ . We also give some positive results including a simpler proof that $c_{0} (ℓ_{1})$ has a unique unconditional basis and a proof that $c_{0} (ℓ_{p_{n}}^{N_{n}})$ has a unique unconditional basis when $p_{n} ￬ 1$ , $N_{n + 1} \geq 2 N_{n}$ and $(p_{n} - p_{n + 1}) l o g N_{n}$ remains bounded.

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

C. Leránoz (1992)

Studia Mathematica

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 $c_{0} (l ₁)$ .

Universal approximations of certain functionals in Banach spaces

P. Přikryl (1974)

Acta Universitatis Carolinae. Mathematica et Physica

Universal series by trigonometric system in weighted $L_{μ}^{1}$ spaces.

Episkoposian, S.A. (2006)

International Journal of Mathematics and Mathematical Sciences

Universal simultaneous approximations of the coefficient functionals

Petr Přikryl (1977)

Časopis pro pěstování matematiky

Variables aléatoires échangeables et espaces d'Orlicz

D. Dacunha-Castelle (1974/1975)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Variables aléatoires échangeables et espaces d'Orlicz (suite)

D. Dacunha-Castelle (1974/1975)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Vector-valued Lp-convergence of orthogonal series and Lagrange interpolation.

Hermann König, Niels J. Nielsen (1994)

Forum mathematicum

Vector-valued multipliers: convolution with operator-valued measures [Book]

Gaudry G. I., Ricker W. J., Jefferies B. R. F. (2000)

Volume estimates and nearly euclidean decompositions for normed spaces

S. J. Szarek (1979/1980)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

$w^{*}$ -basic sequences and reflexivity of Banach spaces

Kamil John (2005)

Czechoslovak Mathematical Journal

We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $ℒ (X, Y)$ is not reflexive for reflexive $X$ and $Y$ then $ℒ (X_{1}, Y)$ is is not reflexive for some $X_{1} \subset X$ , $X_{1}$ having a basis.

W*-algebras on Banach spaces

Peter Legiša (1982)

Studia Mathematica

Walsh subspaces of $L^{p}$ -product spaces

J. Bourgain (1979/1980)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Wavelet bases in $L^{p} (ℝ)$

Gustaf Gripenberg (1993)

Studia Mathematica

It is shown that an orthonormal wavelet basis for $L^{2} (ℝ)$ associated with a multiresolution is an unconditional basis for $L^{p} (ℝ)$ , 1 < p < ∞, provided the father wavelet is bounded and decays sufficiently rapidly at infinity.

Wavelets as Unconditional Bases in L...(...).

P. Wojtaszczyk (1999)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Weak compact generating in duality

Kamil John, Václav Zizler (1976)

Studia Mathematica

Weak compactness and summability

Wojciech Chojnacki (1987)

Mathematica Slovaca

Weakly Compact Generating and Shrinking Markusevic Bases

Fabian, M., Hájek, P., Montesinos, V., Zizler, V. (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B30, 46B03.It is shown that most of the well known classes of nonseparable Banach spaces related to the weakly compact generating can be characterized by elementary properties of the closure of the coefficient space of Markusevic bases for such spaces. In some cases, such property is then shared by all Markusevic bases in the space.

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