Mixed limits of some functional spaces

2019/01/26 by Andrei Novikov, Novikov, Andrei, Zohreh Eskandarian +3
Mathematics · #46A13 #46B70 #46L10 #46L51 #46L52 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1901.09276

openalex publication_date 2019/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we propose a conception of mixed limits of functional spaces as the case, when the upper limit (projective limit of inductive limits) and the lower limit (inductive limit of projective limits) coincide as topological spaces, which are generalization of inductive and projective limits of functional spaces. We show a cases where these mixed limits are naturally obtained as the limit spaces of non-commutative L_p-type spaces associated with the sequence of operators. Also, we obtain results on the properties of limit spaces, we show that limit spaces of Banach algebras are (LF)-spaces, if they converge.

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