Almost euclidean sections in spaces with a symmetric basis

2006 ◽  
pp. 278-288 ◽  
Author(s):  
J. Bourgain ◽  
J. Lindenstrauss
Keyword(s):  
Symmetric Basis

Projection constants of symmetric spaces and variants of Khintchine's inequality

1999 ◽  
Vol 1999 (511) ◽  
pp. 1-42 ◽  
Author(s):  
Hermann König ◽  
Carsten Schütt ◽  
Nicole Tomczak-Jaegermann
Keyword(s):  
Symmetric Spaces ◽  
Dimensional Space ◽  
Complex Case ◽  
Real Case ◽  
The Real ◽  
Symmetric Basis ◽  
Projection Constant ◽  
Khintchine’S Inequality ◽  
Averaging Techniques

Abstract The projection constants of the lpn-spaces for 1 ≦ p ≦ 2 satisfy with in the real case and in the complex case. Further, there is c < 1 such that the projection constant of any n-dimensional space Xn with 1-symmetric basis can be estimated by . The proofs of the results are based on averaging techniques over permutations and a variant of Khintchine's inequality which states that

Banach-Saks index in spaces with symmetric basis

2008 ◽  
Vol 77 (3) ◽  
pp. 396-397 ◽  
Author(s):  
A. I. Novikova ◽  
E. M. Semenov ◽  
F. A. Sukochev
Keyword(s):  
Symmetric Basis

scholarly journals The weak cotype 2 and the Orlicz property of the Lorentz sequence space d(a, 1)

1992 ◽  
Vol 34 (3) ◽  
pp. 271-276
Author(s):  
J. Zhu
Keyword(s):  
Banach Space ◽  
Function Space ◽  
Sequence Space ◽  
Affirmative Answer ◽  
Sequence Spaces ◽  
Similar Question ◽  
Lorentz Sequence Space ◽  
Symmetric Basis ◽  
Orlicz Property

The question “Does a Banach space with a symmetric basis and weak cotype 2 (or Orlicz) property have cotype 2?” is being seriously considered but is still open though the similar question for the r.i. function space on [0, 1] has an affirmative answer. (If X is a r.i. function space on [0, 1] and has weak cotype 2 (or Orlicz) property then it must have cotype 2.) In this note we prove that for Lorentz sequence spaces d(a, 1) they both hold.

A weak Grothendieck compactness principle for Banach spaces with a symmetric basis

Positivity ◽  
2013 ◽  
Vol 18 (1) ◽  
pp. 147-159
Author(s):  
P. N. Dowling ◽  
D. Freeman ◽  
C. J. Lennard ◽  
E. Odell ◽  
B. Randrianantoanina ◽  
...  
Keyword(s):  
Banach Spaces ◽  
Symmetric Basis ◽  
Compactness Principle

Distribution of the Number of Distinct Elements of a Symmetric Basis in a Random $mA$-Sample

1971 ◽  
Vol 16 (3) ◽  
pp. 494-505 ◽  
Author(s):  
V. N. Sachkov
Keyword(s):  
Symmetric Basis

scholarly journals The Trigonometric Polynomial Like Bernstein Polynomial

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Xuli Han
Keyword(s):  
Trigonometric Polynomial ◽  
Bernstein Polynomial ◽  
Bernstein Polynomials ◽  
Trigonometric Polynomials ◽  
Polynomial Space ◽  
Polynomial Sequence ◽  
Symmetric Basis ◽  
Uniformly Convergent

A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of reproducing one degree of trigonometric polynomials are constructed. Some interesting properties of the trigonometric polynomials are given.

scholarly journals A Banach space with a symmetric basis which is of weak cotype 2 but not of cotype 2

2003 ◽  
Vol 157 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Peter G. Casazza ◽  
Niels J. Nielsen
Keyword(s):  
Banach Space ◽  
Symmetric Basis

On Nonreflexive Banach Spaces Which Contain No c0 or lp

1980 ◽  
Vol 32 (6) ◽  
pp. 1382-1389 ◽  
Author(s):  
P. G. Casazza ◽  
Bor-Luh Lin ◽  
R. H. Lohman
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Reflexive Banach Space ◽  
Analytical Description ◽  
Basic Sequence ◽  
Isomorphic Copy ◽  
Uniformly Convex ◽  
Infinite Dimensional ◽  
Symmetric Basis ◽  
Uniformly Convex Space

The first infinite-dimensional reflexive Banach space X such that no subspace of X is isomorphic to c0 or lp, 1 ≦ p < ∞, was constructed by Tsirelson [8]. In fact, he showed that there exists a Banach space with an unconditional basis which contains no subsymmetric basic sequence and which contains no superreflexive subspace. Subsequently, Figiel and Johnson [4] gave an analytical description of the conjugate space T of Tsirelson's example and showed that there exists a reflexive Banach space with a symmetric basis which contains no superreflexive subspace; a uniformly convex space with a symmetric basis which contains no isomorphic copy of lp, 1 < p < ∞; and a uniformly convex space which contains no subsymmetric basic sequence and hence contains no isomorphic copy of lp, 1 < p < ∞. Recently, Altshuler [2] showed that there is a reflexive Banach space with a symmetric basis which has a unique symmetric basic sequence up to equivalence and which contains no isomorphic copy of lp, 1 < p < ∞.

scholarly journals Uniqueness of symmetric basis in quasi-Banach spaces

2008 ◽  
Vol 348 (1) ◽  
pp. 51-54 ◽  
Author(s):  
F. Albiac ◽  
C. Leránoz
Keyword(s):  
Banach Spaces ◽  
Symmetric Basis
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