𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Local Lifting Property for Operator Spaces

✍ Scribed by Seung-Hyeok Kye; Zhong-Jin Ruan

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
322 KB
Volume
168
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

We study the local lifting property for operator spaces. This is a natural noncommutative analogue of the Banach space local lifting property, but is very different from the local lifting property studied in C*-algebra theory. We show that an operator space has the *-local lifting property if and only if it is an L1 1, * space. These operator space are *-completely isomorphic to the operator subspaces of the operator preduals of von Neumann algebras, and thus *-locally reflexive. Moreover, we show that an operator space V has the *-local lifting property if and only if its operator space dual V* is *-injective.

πŸ“œ SIMILAR VOLUMES

Extension Properties for the Space of Co
Extension Properties for the Space of Compact Operators
✍ Timur Oikhberg; Haskell P Rosenthal πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 377 KB

Let Z be a fixed separable operator space, X/Y general separable operator spaces, and T : X Γ„ Z a completely bounded map. Z is said to have the Complete Separable Extension Property (CSEP) if every such map admits a completely bounded extension to Y and the Mixed Separable Extension Property (MSEP)

The bounded approximation property for s
The bounded approximation property for spaces of holomorphic mappings on infinite dimensional spaces
✍ Erhan Γ‡alışkan πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 175 KB πŸ‘ 1 views

## Abstract We study the bounded approximation property for spaces of holomorphic functions. We show that if __U__ is a balanced open subset of a FrΓ©chet–Schwartz space or (__DFM__ )‐space __E__ , then the space ℋ︁(__U__ ) of holomorphic mappings on __U__ , with the compact‐open topology, has the b

Lp-Liouville property for non-local oper
Lp-Liouville property for non-local operators
✍ Jun Masamune; Toshihiro Uemura πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 193 KB

## Abstract The __L^p^__‐Liouville property of a non‐local operator \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {A}$\end{document} is investigated via the associated Dirichlet form \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}