skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Lipschitz geometry of operator spaces and Lipschitz-free operator spaces
Award ID(s):
2055155 1900985
PAR ID:
10526575
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Mathematische Annalen
Volume:
388
Issue:
1
ISSN:
0025-5831
Page Range / eLocation ID:
1053 to 1090
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Abstract Main results of the paper are as follows: (1) For any finite metric space $$M$$ the Lipschitz-free space on $$M$$ contains a large well-complemented subspace that is close to $$\ell _{1}^{n}$$ . (2) Lipschitz-free spaces on large classes of recursively defined sequences of graphs are not uniformly isomorphic to $$\ell _{1}^{n}$$ of the corresponding dimensions. These classes contain well-known families of diamond graphs and Laakso graphs. Interesting features of our approach are: (a) We consider averages over groups of cycle-preserving bijections of edge sets of graphs that are not necessarily graph automorphisms. (b) In the case of such recursive families of graphs as Laakso graphs, we use the well-known approach of Grünbaum (1960) and Rudin (1962) for estimating projection constants in the case where invariant projections are not unique. 
    more » « less
  2. We verify that a large portion of the theory of complex operator spaces and operator algebras (as represented by the 2004 book by the author and Le Merdy for specificity) transfers to the real case. We point out some of the results that do not work in the real case. We also discuss how the theory and standard constructions interact with the complexification, which is often as important, but sometimes much less obvious. For example, we develop the real case of the theory of operator space multipliers and the operator space centralizer algebra, and discuss how these topics connect with complexifi- cation. This turns out to differ in some important details from the complex case. We also characterize real structure in complex operator spaces and give ‘real’ characterizations of some of the most important objects in the subject. 
    more » « less