Barrelled locally convex spaces [E-Book] / Pedro Perez Carreras, Jose Bonet.
Perez Carreras, Pedro.
Bonet, Jose.
Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; 1987
Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,
1 online resource (xv, 512 p.) : ill.
englisch
9780444701299
044470129X
North-Holland mathematics studies ; 131
Notas de matematica ; 113
Full Text
This book is a systematic treatment of barrelled spaces, and of structures in which barrelledness conditions are significant. It is a fairly self-contained study of the structural theory of those spaces, concentrating on the basic phenomena in the theory, and presenting a variety of functional-analytic techniques. Beginning with some basic and important results in different branches of Analysis, the volume deals with Baire spaces, presents a variety of techniques, and gives the necessary definitions, exploring conditions on discs to ensure that they are absorbed by the barrels of the space. The abstract theory of barrelled spaces is then presented, as well as local completeness and its applications to the inheritance of the Mackey topology to subspaces. Further discussed is the abstract study of bornological and ultrabornological spaces; B- and B-completeness; inductive limits; strong barrelledness conditions; characterizations of barrelled, bornological and (DF)-spaces in the context of spaces of type C(X); the stability of barrelledness conditions of topological tensor products and the related questions of commutability of inductive limits and tensor products; and the holomorphically significant properties of locally convex spaces as developed by Nachbin and others.