|
|
|
|
|
Continuity of
spectral functions and the lakes of Wada
Domingo Antonio Herrero |
|
Vol. 113 (1984), No. 2, 365–371
|
Abstract |
|
The functions σ, mapping a Hilbert space operator T into its spectrum σ(T), or σe (defined by σe(T) = essential spectrum of T), or ρsh −F(T) mapping T into the set of complex numbers λ such that λ − T is semi-Fredholm of index h, etc, have a very erratic behavior. They are continuous on a dense set of operators and discontinuous on another dense set of operators. It is not completely apparent, however, that all of them are simultaneously continuous on a certain dense subset and simultaneously discontinuous on another dense subset. |
Mathematical Subject Classification 2000
Primary: 47A10
|
Milestones
Received: 31 August 1982
Revised: 5 January 1983
Published: 1 August 1984
|
Authors |
| Domingo Antonio Herrero | |
|
