Results 11 to 20 of about 604,967 (307)
Essential numerical range and $C$-numerical range for unbounded operators [PDF]
Studia Mathematica, 2022 Consider an unbounded operator \(T\) on a Hilbert space \(\mathcal{H}\). The authors introduce a new type of essential numerical range for \(T\), called \(W_{e5}(T)\) (essential numerical range of type 5). They show, for instance, that \(W_{e5}(T)\) is closed, convex, and contains the essential spectrum \(\sigma_e(T)\).
Hefti, Nicolas Benjamin +1 more
openaire +4 more sources
The numerical range and the essential numerical range [PDF]
Proceedings of the American Mathematical Society, 1977 A simple proof is given of Lancaster’s theorem that the convex hull of the numerical and essential numerical ranges of a Hilbert space operator is the closure of the numerical range.
J. P. Williams
core +3 more sources
On the Numerical Range and Numerical Radius of the Volterra Operator
Известия Иркутского государственного университета: Серия "Математика", 2018 In this paper, we investigated the numerical range and the numerical radius of the classical Volterra operator on the complex space $L^2[0,1]$. In particular, we determined the numerical range, the numerical radius of real and imaginary part of the ...
L. Khadkhuu, D. Tsedenbayar
doaj +3 more sources
Numerical Range of Moore–Penrose Inverse Matrices
Mathematics, 2020 Let A be an n-by-n matrix. The numerical range of A is defined as W ( A ) = { x * A x : x ∈ C n , x * x = 1 } . The Moore–Penrose inverse A + of A is the unique matrix satisfying A A + A = A , A + A A + = A ...
Mao-Ting Chien
doaj +3 more sources
The joint numerical range and the joint essential numerical range
, 2015 Let B(H) denote the algebra of bounded linear operators on a complex Hilbert space H. The (classical) numerical range of T ∈ B(H) is the set W(T) = {〈T x; x〉: x ∈ H; ‖x‖ = 1} Writing T= T_1 + iT_2 for self-adjoint T_1, T_2 ∈ B(H), W(T) can be identified with the set {(〈T_1 x, x〉,〈T_2 x, x〉) : x ∈ H, ‖x‖ = 1}.
林梓萌., Lam, Tsz-mang.
openaire +3 more sources
Numerical Range and Quadratic Numerical Range for Damped Systems [PDF]
, 2017 We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations $\ddot{z}(t) + D \dot{z} (t) + A_0 z(t) = 0$ in a Hilbert space. Our main tool is the quadratic numerical range for which we establish the spectral inclusion property under weak assumptions on the operators involved ...
Jacob, Birgit +3 more
openaire +3 more sources
Computing the q-Numerical Range of Differential Operators
Journal of Applied Mathematics, 2020 A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of thez Hilbert space. In this paper, we establish an approximation of the q-numerical range of bounded and unbounnded operator matrices by ...
Ahmed Muhammad, Faiza Abdullah Shareef
doaj +5 more sources
Index rank-$k$ numerical range of matrices [PDF]
Journal of Mahani Mathematical Research, 2023 We introduce the $\alpha-$higher rank form of the matrix numerical range, which is a special case of the matrix polynomial version of higher rank numerical range.
Sharifeh Rezagholi, Rouholah Yasini
doaj +1 more source
Further extensions of Hartfiel’s determinant inequality to multiple matrices
Special Matrices, 2021 Following the recent work of Zheng et al., in this paper, we first present a new extension Hartfiel’s determinant inequality to multiple positive definite matrices, and then we extend the result to a larger class of matrices, namely, matrices whose ...
Luo Wenhui
doaj +1 more source
The Numerical Range of C*ψ Cφ and Cφ C*ψ
Concrete Operators, 2021 In this paper we investigate the numerical range of C*bφm Caφn and Caφn C*bφm on the Hardy space where φ is an inner function fixing the origin and a and b are points in the open unit disc.
Clifford John +2 more
doaj +1 more source