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

Studia Mathematica (1994)

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

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topTerenzi, 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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