Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 274-277
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V. I. Gurarii. The existence of a non-hereditarily complete family in an arbitrary separable Banach space. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part IX, Tome 92 (1979), pp. 274-277. http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a19/
@article{ZNSL_1979_92_a19,
author = {V. I. Gurarii},
title = {The existence of a~non-hereditarily complete family in an arbitrary separable {Banach} space},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {274--277},
year = {1979},
volume = {92},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a19/}
}
TY - JOUR
AU - V. I. Gurarii
TI - The existence of a non-hereditarily complete family in an arbitrary separable Banach space
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1979
SP - 274
EP - 277
VL - 92
UR - http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a19/
LA - ru
ID - ZNSL_1979_92_a19
ER -
%0 Journal Article
%A V. I. Gurarii
%T The existence of a non-hereditarily complete family in an arbitrary separable Banach space
%J Zapiski Nauchnykh Seminarov POMI
%D 1979
%P 274-277
%V 92
%U http://geodesic.mathdoc.fr/item/ZNSL_1979_92_a19/
%G ru
%F ZNSL_1979_92_a19
It is proved that every separable Banach space $E$ contains a complete minimal family $\{x_j\}_1^\infty$ with the total biorthogonal family $\{f_j\}_1^\infty$ (in $E^*$) but not hereditarily complete (this means that the closed linear envelope of the f amily $\{f_j(z)x_j\}_1^\infty)$ does not coincide with $E$).
