Neumann, Michael M. On local spectral properties of operators on Banach spaces. (English) Zbl 0929.47001 Aiena, P. (ed.) et al., International workshop on Operator theory, Cefalù, Italy, July 14–19, 1997. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 56, 15-25 (1998). Local spectral theory is a well established sector of research in modern operator theory [see N. Dunford and J. Schwartz, “Linear operators. Part III”, New York (1971; Zbl 0243.47001)]. The note under review is a lucid account of recent developments in this area; specifically, the author discusses the interplay between Bishop’s property \((\beta)\) and Dunford’s property C, with emphasis on examples chosen among weighted shifts.A compulsory reading for all readers interested in local spectral theory in a single variable.For the entire collection see [Zbl 0911.00033]. Reviewer: Mihai Putinar (Santa Barbara) Cited in 1 ReviewCited in 5 Documents MSC: 47A11 Local spectral properties of linear operators 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) Keywords:weighted shift; local spectral theory; Bishop’s property \((\beta)\); Dunford’s property C Citations:Zbl 0243.47001 PDFBibTeX XMLCite \textit{M. M. Neumann}, in: International workshop on Operator theory, Cefalù, Italy, July 14--19, 1997. Palermo: Circolo Matematico di Palermo. 15--25 (1998; Zbl 0929.47001)