Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis

Paolo Terenzi

Studia Mathematica (1994)

  • Volume: 111, Issue: 3, page 207-222
  • ISSN: 0039-3223

Abstract

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Every separable, infinite-dimensional Banach space X has a biorthogonal sequence z n , z * n , with s p a n z * n norming on X and ∥ z n ∥ + ∥ z * n ∥ bounded, so that, for every x in X and x* in X*, there exists a permutation π(n) of n so that x ∈ c o n v ¯ f i n i t e s u b s e r i e s o f ∑ n = 1 ∞ z * n ( x ) z n a n d x * n ( x ) = ∑ n = 1 ∞ z * π ( n ) ( x ) x * ( z π ( n ) ) .

How to cite

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Terenzi, Paolo. "Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis." Studia Mathematica 111.3 (1994): 207-222. <http://eudml.org/doc/216129>.

@article{Terenzi1994,
abstract = {Every separable, infinite-dimensional Banach space X has a biorthogonal sequence $\{z_n, z*_n\}$, with $span\{z*_n\}$ norming on X and $\{∥z_n∥ + ∥z*_n∥\}$ bounded, so that, for every x in X and x* in X*, there exists a permutation π(n) of n so that $x ∈ \overline\{conv\} \{finite subseries of ∑_\{n=1\}^\{∞\} z*_n(x)z_n\} and x*_n(x) = ∑_\{n=1\}^∞ z*_\{π(n)\}(x)x*(z_\{π(n)\})$.},
author = {Terenzi, Paolo},
journal = {Studia Mathematica},
keywords = {biorthogonal sequence},
language = {eng},
number = {3},
pages = {207-222},
title = {Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis},
url = {http://eudml.org/doc/216129},
volume = {111},
year = {1994},
}

TY - JOUR
AU - Terenzi, Paolo
TI - Every separable Banach space has a bounded strong norming biorthogonal sequence which is also a Steinitz basis
JO - Studia Mathematica
PY - 1994
VL - 111
IS - 3
SP - 207
EP - 222
AB - Every separable, infinite-dimensional Banach space X has a biorthogonal sequence ${z_n, z*_n}$, with $span{z*_n}$ norming on X and ${∥z_n∥ + ∥z*_n∥}$ bounded, so that, for every x in X and x* in X*, there exists a permutation π(n) of n so that $x ∈ \overline{conv} {finite subseries of ∑_{n=1}^{∞} z*_n(x)z_n} and x*_n(x) = ∑_{n=1}^∞ z*_{π(n)}(x)x*(z_{π(n)})$.
LA - eng
KW - biorthogonal sequence
UR - http://eudml.org/doc/216129
ER -

References

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