ArticleOriginal scientific text

Title

Rearrangement of series in nonnuclear spaces

Authors 1

Affiliations

  1. Institute of Mathematics, Łódź University 90-238 Łódź, Poland

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.

Keywords

rearrangement of series, Lévy-Steinitz theorem

Bibliography

  1. M. Banaszczyk and W. Banaszczyk, Characterization of nuclear spaces by means of additive subgroups, Math. Z. 186 (1984), 125-133.
  2. W. Banaszczyk, The Steinitz theorem on rearrangement of series for nuclear spaces, J. Reine Angew. Math. 403 (1990), 187-200.
  3. W. Banaszczyk and J. Grabowski, Connected subgroups of nuclear spaces, Studia Math. 78 (1984), 161-163.
Pages:
213-222
Main language of publication
English
Received
1991-03-13
Accepted
1993-06-22
Published
1993
Exact and natural sciences