Open AccessMETRIC AND TOPOLOGICAL FREEDOM FOR SEQUENTIAL OPERATOR SPACES
Author(s) -
N. T. Nemesh,
S. M. Shteiner
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-10-55-67
Subject(s) - operator (biology) , mathematics , metric space , characterization (materials science) , metric (unit) , space (punctuation) , pure mathematics , algebra over a field , computer science , biochemistry , chemistry , operations management , repressor , transcription factor , economics , gene , operating system , materials science , nanotechnology
In 2002 Anselm Lambert in his PhD thesis [1] introduced the denition of sequential operator space and managed to establish a considerable amount of analogs of corresponding results in operator space theory. Informally speaking, the category of sequential operator spaces is situated ”between” the categories of normed and operator spaces. This article aims to describe free and cofree objects for dierent versions of sequential operator space homology. First of all, we will show that duality theory in above-mentioned category is in many respects analogous to that in the category of normed spaces. Then, based on those results, we will give a full characterization of both metric and topological free and cofree objects.