On certain extension properties for the space of compact operators

Let $Z$ be a fixed separable operator space, $X\subset Y$ general separable operator spaces, and $T:X\to Z$ 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 $Y$; the Mixed Separable Extension Property (MSEP) if every such $T$ admits a bounded extension to $Y$. Finally, $Z$ is said to have the Complete Separable Complementation Property (CSCP) if $Z$ is locally reflexive and $T$ admits a completely bounded extension to $Y$ provided $Y$ is locally reflexive and $T$ is a complete surjective isomorphism. Let ${\bf K}$ denote the space of compact operators on separable Hilbert space and ${\bf K}_0$ the $c_0$ sum of {\Cal M}_n's (the space of ``small compact operators''). It is proved that ${\bf K}$ has the CSCP, using the second author's previous result that ${\bf K}_0$ has this property. A new proof is given for the result (due to E. Kirchberg) that ${\bf K}_0$ (and hence ${\bf K}$) fails the CSEP. It remains an open question if ${\bf K}$ has the MSEP; it is proved this is equivalent to whether ${\bf K}_0$ has this property. A new Banach space concept, Extendable Local Reflexivity (ELR), is introduced to study this problem. Further complements and open problems are discussed.Comment: 71 pages, AMSTe

Industrial Relations in Greenfield Sites

There is a popular stereotype that at greenfield sites managers practice, and sustain over time new forms of human resource management and that in doing so they obtain highly positive performance outcomes. A persisting theme in this stereotype is that greenfield sites are characterised by a highly collaborative form of employee relations and that they are largely strike and conflict free. The aim of this paper is to test the stereotype by reviewing what is known about the subject. Existing research on greenfield sites is places within a broad conceptual framework, key issues are highlighted and gaps in our knowledge identified. The discussion in foreign-owned firms; how well greenfield sites cope with the ageing process; and the industrial relations and human resource outcomes obtained in greenfield sites. The review finds that most research ignores the last two issues. At present it is impossible to conclude with confidence that IR/HR practices adopted in these firms are any more effective than traditional systems. There is also little or no evidence about how greenfield site practices adapt over time. The review provides the point of departures for research being undertaken at the LSE's Centre for Economic Performance; the research agenda is briefly discussed.