- #1
SemM
Gold Member
- 195
- 13
Hi, why do unbounded operators and bounded operators differ so much in terms of defining their spectra?
1. The unbounded operator requires a self-adjoint extension to define its spectrum.
2. A bounded one does not require a self-adjoint extension to define the spectral properties.
3. Still the unbounded operator is bounded within its domain and should be defined accordingly.Why can't the spectral properties be defined in the unbounded operators domain by the same method as for bounded operators?
1. The unbounded operator requires a self-adjoint extension to define its spectrum.
2. A bounded one does not require a self-adjoint extension to define the spectral properties.
3. Still the unbounded operator is bounded within its domain and should be defined accordingly.Why can't the spectral properties be defined in the unbounded operators domain by the same method as for bounded operators?