|
|
| |
| Geometry of Numerical Range of Linear Operator Polynomial |
| |
Citation： |
Deyu WU,Alatancang CHEN.Geometry of Numerical Range of Linear Operator Polynomial[J].Chinese Annals of Mathematics B,2025,46(1):151~162 |
| Page view： 179
Net amount： 179 |
Authors： |
Deyu WU; Alatancang CHEN |
Foundation： |
the National Natural Science Foundation of China (No. 11561048) and the
Natural Science Foundation of Inner Mongolia (No. 2023MS01011). |
|
|
| Abstract： |
Let B(X) be the algebra of all bounded linear operators on a Hilbert space X.
Consider an operator polynomial
P(λ) = Amλm + Am?1λm?1 + · · · + A0,
where Ai ∈ B(X), i = 0, 1, · · · , m. The numerical range of P(λ) is defined as
W (P(λ)) = {λ ∈ C : (P(λ)x, x) = 0 for some x 6= 0}.
The main goal of this paper is to respond to an open problem proposed by professor Li, and
determine general conditions on connectivity, convexity and spectral inclusion property of
W (P(λ)). They also consider the relationship between operator polynomial numerical
range and block numerical range. |
Keywords： |
Linear operator polynomial Numerical range Connectedness Convexity Block numerical range |
Classification： |
47A12 |
|
|
Download PDF Full-Text
|
|
|
|
