Cantor–Bernstein theorems for certain symmetric bases in Banach spaces

2015 ◽  
Vol 105 (5) ◽  
pp. 425-433
Author(s):  
Marcos J. González
Keyword(s):  
Banach Spaces ◽  
Symmetric Bases

scholarly journals On symmetric bases in nonseparable Banach spaces

1987 ◽  
Vol 85 (2) ◽  
pp. 157-161 ◽  
Author(s):  
Lech Drewnowski
Keyword(s):  
Banach Spaces ◽  
Symmetric Bases

scholarly journals On Perfectly Homogeneous Bases in Quasi-Banach Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-7
Author(s):  
F. Albiac ◽  
C. Leránoz
Keyword(s):  
Banach Spaces ◽  
Classical Result ◽  
Unit Vector ◽  
Unit Vector Basis ◽  
Vector Basis ◽  
Symmetric Bases ◽  
Special Case

For0<p<∞the unit vector basis ofℓphas the property of perfect homogeneity: it is equivalent to all its normalized block basic sequences, that is, perfectly homogeneous bases are a special case of symmetric bases. For Banach spaces, a classical result of Zippin (1966) proved that perfectly homogeneous bases are equivalent to either the canonicalc0-basis or the canonicalℓp-basis for some1≤p<∞. In this note, we show that (a relaxed form of) perfect homogeneity characterizes the unit vector bases ofℓpfor0<p<1as well amongst bases in nonlocally convex quasi-Banach spaces.

scholarly journals Lipschitz symmetric functions on Banach spaces with symmetric bases

2021 ◽  
Vol 13 (3) ◽  
pp. 727-733
Author(s):  
M.V. Martsinkiv ◽  
S.I. Vasylyshyn ◽  
T.V. Vasylyshyn ◽  
A.V. Zagorodnyuk
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Symmetric Functions ◽  
Large Family ◽  
Symmetric Polynomials ◽  
Symmetric Basis ◽  
Several Variables ◽  
Symmetric Bases ◽  
Unbounded Subset

We investigate Lipschitz symmetric functions on a Banach space $X$ with a symmetric basis. We consider power symmetric polynomials on $\ell_1$ and show that they are Lipschitz on the unbounded subset consisting of vectors $x\in \ell_1$ such that $|x_n|\le 1.$ Using functions $\max$ and $\min$ and tropical polynomials of several variables, we constructed a large family of Lipschitz symmetric functions on the Banach space $c_0$ which can be described as a semiring of compositions of tropical polynomials over $c_0$.

scholarly journals Projections on Banach spaces with symmetric bases

1974 ◽  
Vol 52 (2) ◽  
pp. 189-193 ◽  
Author(s):  
P. Casazza ◽  
Bor Lin
Keyword(s):  
Banach Spaces ◽  
Symmetric Bases

Fredholm Theory in Banach Spaces

1986 ◽  
Author(s):  
Anthony Francis Ruston
Keyword(s):  
Banach Spaces ◽  
Fredholm Theory
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