Rearrangement of series in nonnuclear spaces
Studia Mathematica (1993)
- Volume: 107, Issue: 3, page 213-222
- ISSN: 0039-3223
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Abstract
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topBanaszczyk, Wojciech. "Rearrangement of series in nonnuclear spaces." Studia Mathematica 107.3 (1993): 213-222. <http://eudml.org/doc/216030>.
@article{Banaszczyk1993,
abstract = {It is proved that if a metrizable locally convex space is not nuclear, then it does not satisfy the Lévy-Steinitz theorem on rearrangement of series.},
author = {Banaszczyk, Wojciech},
journal = {Studia Mathematica},
keywords = {rearrangement of series; Lévy-Steinitz theorem; metrizable locally convex space},
language = {eng},
number = {3},
pages = {213-222},
title = {Rearrangement of series in nonnuclear spaces},
url = {http://eudml.org/doc/216030},
volume = {107},
year = {1993},
}
TY - JOUR
AU - Banaszczyk, Wojciech
TI - Rearrangement of series in nonnuclear spaces
JO - Studia Mathematica
PY - 1993
VL - 107
IS - 3
SP - 213
EP - 222
AB - It is proved that if a metrizable locally convex space is not nuclear, then it does not satisfy the Lévy-Steinitz theorem on rearrangement of series.
LA - eng
KW - rearrangement of series; Lévy-Steinitz theorem; metrizable locally convex space
UR - http://eudml.org/doc/216030
ER -
References
top- [1] M. Banaszczyk and W. Banaszczyk, Characterization of nuclear spaces by means of additive subgroups, Math. Z. 186 (1984), 125-133. Zbl0526.46004
- [2] W. Banaszczyk, The Steinitz theorem on rearrangement of series for nuclear spaces, J. Reine Angew. Math. 403 (1990), 187-200. Zbl0682.46002
- [3] W. Banaszczyk and J. Grabowski, Connected subgroups of nuclear spaces, Studia Math. 78 (1984), 161-163. Zbl0537.46007
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