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On a Class of Nuclear Spaces, II

✍ Scribed by Gottfried Köthe

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
426 KB
Volume
119
Category
Article
ISSN
0025-584X

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✦ Synopsis

It was about 1932 that TOEPLITZ and I discovered the convergence-free spaces, the first general results appeared in [7]. F. NENN, a student of mine, studied in [8] the spaces of finite degree. I generalized his theory to the class of spaces of countable degree in [Z].

Further progress seemed at that time difficult. Some of these spaces, in particular qw$wrp, became of general interest. I returned only recently to these old problems and was able in part I (see [6]) to determine the sequence space structure of the spaces e&, p), where L and p are spaces of finite degree.

In this note I continue the study of convergence-free spaces and collect some observations and some new results. I will use the notations and results of [2] and The motivation for my interest in this class of nuclear spaces lies in the fact that this class has a pronounced algebraic character in sharp contrast to the class of ~JAKACH spaces which are fundamental structures in analysis.

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