On Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space

DOI10.1080/0308108031000134981zbMath1059.15029OpenAlexW1964014207MaRDI QIDQ4818362

Natália Bebiano, João da Providência, Graça Soares, Rute Lemos

Publication date: 28 September 2004

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/0308108031000134981

zbMATH Keywords

numerical rangeHermitian matrixindefinite inner product space

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Quadratic and bilinear forms, inner products (15A63) Linear operators on spaces with an indefinite metric (47B50)

Related Items (18)

Spectral properties and numerical range of off-diagonal infinite-dimensional Hamiltonian operators ⋮ An extension of Birkhoff's theorem with an application to determinants ⋮ The numerical range of non-negative operators in Krein spaces ⋮ Computing the S-numerical ranges of differential operators ⋮ Ratio numerical ranges of operators ⋮ Flat portions on the boundary of the indefinite numerical range of \(3\times 3\) matrices ⋮ The \(J\)-numerical range of a \(J\)-Hermitian matrix and related inequalities ⋮ Numerical ranges of unbounded operators arising in quantum physics. ⋮ Computing the numerical range of Krein space operators ⋮ An inverse indefinite numerical range problem ⋮ More on geometry of Krein space \(C\)-numerical range ⋮ Spectral inclusion properties of the numerical range in a space with an indefinite metric ⋮ On the geometry of numerical ranges in spaces with an indefinite inner product ⋮ Indefinite higher-rank numerical ranges ⋮ Indefinite numerical range of 3 × 3 matrices ⋮ The numerical range of banded 2-Toeplitz operators in spaces with an indefinite metric ⋮ Inequalities for \(J\)-Hermitian matrices ⋮ \(J\)-orthostochastic matrices of size \(3 \times 3\) and numerical ranges of Krein space operators

Uses Software

• Matlab

Cites Work

• On the numerical range of a bounded operator
• Some analogies between the c-numerical range and a certain variation on this concept
• On a conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two Hermitian matrices. I
• A conjecture of Kippenhahn about the characteristic polynomial of a pencil generated by two hermitian matrices. II
• Elementary inclusion relations for generalized numerical ranges
• On a minimax equality for seminorms
• Computer generated numerical ranges and some resulting theorems
• Nondifferentiabie points of ∂W_c(A)
• Numerical Determination of the Field of Values of a General Complex Matrix
• On the Field of Values of a Square Matrix
• Remarks on numerical ranges of operators in spaces with an indefinite metric
• On the boundary of theC-numerical range of a matrix
• Über den Wertevorrat einer Matrix

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