|
|
| |
| Essential Numerical Ranges of Linear Relations and Singular Discrete Linear Hamiltonian Systems |
| |
Citation： |
Li ZHU,Huaqing SUN.Essential Numerical Ranges of Linear Relations and Singular Discrete Linear Hamiltonian Systems[J].Chinese Annals of Mathematics B,2025,46(1):63~84 |
| Page view： 192
Net amount： 181 |
Authors： |
Li ZHU; Huaqing SUN |
Foundation： |
the National Natural Science Foundation of China (No. 11971262), Shandong
Province Natural Science Foundation (No. ZR2019MA038, ZR2024QA088) |
|
|
| Abstract： |
In the paper, a concept of the essential numerical range We(T ) of a linear
relation T in a Hilbert space is given, other various essential numerical ranges Wei(T ),
i = 1, 2, 3, 4, are introduced, and relationships among We(T ) and Wei(T ) are established.
These results generalize relevant results obtained by B?gli et al. in [B?gli, S., Marletta, M.
and Tretter, C., The essential numerical range for unbounded linear operators, J. Funct.
Anal., 279, 2020, 47–12]. Moreover, several fundamental properties of closed relations
related to its operator parts are presented. In addition, singular discrete linear Hamiltonian
systems including non-symmetric cases are considered, several properties for the associated
minimal relations H0 are derived, and the above results for abstract linear relations are
applied to H0. |
Keywords： |
Linear relation Numerical range Essential numerical range Essential
spectrum Singular discrete linear Hamiltonian system |
Classification： |
47A06, 47A12, 39A70 |
|
|
Download PDF Full-Text
|
|
|
|
