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ArticleOriginal scientific text

Title

Factorization of Montel operators

Authors 1, 2

Affiliations

  1. FB IV Mathematik, Universität Trier, W-5500 Trier, Germany
  2. Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Abstract

Consider the following conditions. (a) Every regular LB-space is complete; (b) if an operator T between complete LB-spaces maps bounded sets into relatively compact sets, then T factorizes through a Montel LB-space; (c) for every complete LB-space E the space C (βℕ, E) is bornological. We show that (a) ⇒ (b) ⇒ (c). Moreover, we show that if E is Montel, then (c) holds. An example of an LB-space E with a strictly increasing transfinite sequence of its Mackey derivatives is given.

Keywords

ENG
Fréchet space, Fréchet-Montel space, complete LB-space, Montel LB-space, regular LB-space, Mackey completion of an LB-space, bornologicity of C(K,E)

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Studia Mathematica
1993/107/1
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Pages:
15-32
Main language of publication
English
Received
1992-08-21
Published
1993
Exact and natural sciences