Displaying similar documents to “Shapes and computer generation of numerical ranges of Krein space operators.”

Computing the numerical range of Krein space operators

Natalia Bebiano, J. da Providência, A. Nata, J.P. da Providência (2015)

Open Mathematics

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Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their...

On numerical range of sp(2n, C)

Wen Yan, Jicheng Tao, Zhao Lu (2016)

Special Matrices

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In this paper we studied the classical numerical range of matrices in sp(2n, C). We obtained some result on the relationship between the numerical range of a matrix in and that [...] of its diagonal block, the singular values of its off-diagonal block A2.

Numerical index with respect to an operator

Mohammad Ali Ardalani (2014)

Studia Mathematica

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We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.

The Bishop-Phelps-Bollobás property for numerical radius in ℓ₁(ℂ)

Antonio J. Guirao, Olena Kozhushkina (2013)

Studia Mathematica

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We show that the set of bounded linear operators from X to X admits a Bishop-Phelps-Bollobás type theorem for numerical radius whenever X is ℓ₁(ℂ) or c₀(ℂ). As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for ℓ₁(ℂ).