More Like this

1. Lipschitz geometry of operator spaces and Lipschitz-free operator spaces

   https://doi.org/10.1007/s00208-022-02518-1  

   Braga, Bruno M; Chávez-Domínguez, Javier Alejandro; Sinclair, Thomas (January 2024, Mathematische Annalen)
2. Real operator spaces and operator algebras

   https://doi.org/10.4064/sm230329-23-12  

   Blecher, David P (January 2024, Studia Mathematica)

   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
3. Notes on Real Interpolation of Operator Lp-Spaces

   https://doi.org/10.1007/s10473-021-0622-2  

   Junge, Marius; Xu, Quanhua (November 2021, Acta Mathematica Scientia)
4. On the small scale nonlinear theory of operator spaces

   https://doi.org/10.5802/crmath.678  

   Braga, Bruno M; Chávez-Domínguez, Javier Alejandro (December 2024, Comptes Rendus. Mathématique)

   We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be $ℝ$-linear. We obtain a generalization of the aforementioned result to completely coarse maps defined on the unit ball of an operator space. By relaxing the condition to a small scale one, we prove that there are many non-linear examples of maps which are completely Lipschitz in small scale. We define a geometric parameter for homogeneous Hilbertian operator spaces which imposes restrictions on the existence of such maps. 

   more » « less
5. Dilations of operator-valued measures with bounded p -variations and framings on Banach spaces

   https://doi.org/10.1016/j.jfa.2018.01.006  

   Han, Deguang; Larson, David R.; Liu, Rui (March 2018, Journal of Functional Analysis)