A condition of isomorphism of a~Banach space with the Orlicz property to a~Hilbert space
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XII, Tome 126 (1983), pp. 138-142
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It is proved, that a Banach space $X$ with the Orlicz property is isomorphic to a Hilbert space if and only if in the class $C^2(X)$ there exists a nonzero function with a bounded support.
@article{ZNSL_1983_126_a14,
author = {B. M. Makarov},
title = {A condition of isomorphism of {a~Banach} space with the {Orlicz} property to {a~Hilbert} space},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {138--142},
publisher = {mathdoc},
volume = {126},
year = {1983},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a14/}
}
TY - JOUR AU - B. M. Makarov TI - A condition of isomorphism of a~Banach space with the Orlicz property to a~Hilbert space JO - Zapiski Nauchnykh Seminarov POMI PY - 1983 SP - 138 EP - 142 VL - 126 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a14/ LA - ru ID - ZNSL_1983_126_a14 ER -
B. M. Makarov. A condition of isomorphism of a~Banach space with the Orlicz property to a~Hilbert space. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XII, Tome 126 (1983), pp. 138-142. http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a14/