Every separable Banach space has a basis with uniformly controlled permutations

Paolo Terenzi. Every separable Banach space has a basis with uniformly controlled permutations. 2006. <http://eudml.org/doc/286047>.

@book{PaoloTerenzi2006,
abstract = {There exists a universal control sequence $\{p̅(m)\}_\{m=1\}^\{∞\}$ of increasing positive integers such that: Every infinite-dimensional separable Banach space X has a biorthogonal system xₙ,xₙ* with ||xₙ|| = 1 and ||xₙ*|| < K for each n such that, for each x ∈ X, $x = ∑_\{n=1\}^\{∞\} x_\{π(n)\}*(x)x_\{π(n)\}$ where π(n) is a permutation of n which depends on x but is uniformly controlled by $\{p̅(m)\} _\{m=1\}^\{∞\}$, that is, $n_\{n=1\}^\{m\} ⊆ π(n)_\{n=1\}^\{p̅(m)\} ⊆ n_\{n=1\}^\{p̅(m+1)\}$ for each m.},
author = {Paolo Terenzi},
keywords = {biorthogonal system; basis with individual brackets; basis with individual permutations; separable Banach space},
language = {eng},
title = {Every separable Banach space has a basis with uniformly controlled permutations},
url = {http://eudml.org/doc/286047},
year = {2006},
}

TY - BOOK
AU - Paolo Terenzi
TI - Every separable Banach space has a basis with uniformly controlled permutations
PY - 2006
AB - There exists a universal control sequence ${p̅(m)}_{m=1}^{∞}$ of increasing positive integers such that: Every infinite-dimensional separable Banach space X has a biorthogonal system xₙ,xₙ* with ||xₙ|| = 1 and ||xₙ*|| < K for each n such that, for each x ∈ X, $x = ∑_{n=1}^{∞} x_{π(n)}*(x)x_{π(n)}$ where π(n) is a permutation of n which depends on x but is uniformly controlled by ${p̅(m)} _{m=1}^{∞}$, that is, $n_{n=1}^{m} ⊆ π(n)_{n=1}^{p̅(m)} ⊆ n_{n=1}^{p̅(m+1)}$ for each m.
LA - eng
KW - biorthogonal system; basis with individual brackets; basis with individual permutations; separable Banach space
UR - http://eudml.org/doc/286047
ER -