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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].

MSC:

47A11 Local spectral properties of linear operators
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Citations:

Zbl 0243.47001
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