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An introduction to locally convex inductive limits. (English) Zbl 0786.46001
Functional analysis and its applications, Lect. Int. Sch., Nice/Fr. 1986, 35-133 (1988).
[For the entire collection see Zbl 0731.00014.]
Inductive limits of locally convex spaces come up to many places in theory and applications. The article under review gives a good introduction and a comprehensive survey on the essential effects and results. Its main topics are strict inductive limits, weakly compact, compact and nuclear inductive limits; \((LF)\)- and \((LB)\)-spaces and related regularity properties as well as applications to Köthe sequence spaces and the projective description of weighted inductive limits. Many interesting examples and counterexamples are included. Since the publication of the article further progress in understanding \((LF)\)- spaces has been achieved in D. Vogt, Regularity properties of \((LF)\)-spaces, in “Progress in functional analysis”, North-Holland Math. Studies 170, 57-84 (1992).

46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46M40 Inductive and projective limits in functional analysis