This article is cited in 61 papers

Homological methods in the theory of locally convex spaces

V. P. Palamodov


Abstract: This paper deals with the categories of direct and inverse countable spectra of locally convex spaces and with the functors of inductive and projective limits defined on these categories. We study the homological properties of such functors, introduce their satellites, and search for conditions for these satellites to vanish. We then apply the accumulated information about the functors of the limiting processes to certain problems in the theory of locally convex spaces: topological properties of a locally convex inductive limit, the homomorphism of the adjoint operator, the possibility of extending and lifting a map and the properties of the augmentation functor. We also consider examples of certain “pathologies”.

UDC: 513.83

MSC: 46M15, 46A03, 46A13, 46M40

Received: 04.05.1970

 English version: Russian Mathematical Surveys, 1971, 26:1, 1–64

Bibliographic databases:

• 
•