A generalized numerical range: the range of a constrained sesquilinear form

DOI10.1080/03081089408818311zbMath0819.15018OpenAlexW2046783138MaRDI QIDQ4322507

Chi-Kwong Li, Leiba Rodman, Paras P. Mehta

Publication date: 9 February 1995

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

Full work available at URL: https://doi.org/10.1080/03081089408818311

zbMATH Keywords

Hilbert spacelinear operatorslinear preservers\(q\)-numerical rangesesquilinear form\(q\)-numerical radius

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)

Related Items (25)

Unitary similarity invariant function preservers of skew products of operators ⋮ Grüss inequality for completely bounded maps ⋮ The q-numerical range and the Davis-Wielandt shell of reducible 3 × 3 matrices ⋮ Some aspects of the theory of norms ⋮ A distance formula for tuples of operators ⋮ Multiplicative Preservers of C-Numerical Ranges and Radii ⋮ The inverse \(q\)-numerical range problem and connections to the Davis-Wielandt shell and the pseudospectra of a matrix ⋮ q -Numerical radius inequalities for Hilbert space ⋮ Between the von Neumann inequality and the Crouzeix conjecture ⋮ Birkhoff-James approximate orthogonality sets and numerical ranges ⋮ The Birkhoff-James orthogonality in Hilbert \(C^{\ast }\)-modules ⋮ Unnamed Item ⋮ Isometries of a generalized numerical radius on compact operators ⋮ On theq-numerical range of matrices and matrix polynomials ⋮ Isometries of a generalized numerical radius ⋮ Invertible preservers and algebraic groups III: preservers of unitary similarity (congruence) invariants and overgroups of some unitary subgroups^∗ ⋮ Sesquilinear version of numerical range and numerical radius ⋮ q-numerical ranges of normal and convex matrices ⋮ Some Results on the q-Numerical ⋮ Davis-Wielandt shell and \(q\)-numerical range ⋮ On the stability of the orthogonality equation and the orthogonality-preserving property with two unknown functions ⋮ \(a\)-numerical range on \(C^{\ast}\)-algebras ⋮ Theq-numerical range of matrix polynomials ⋮ A numerical investigation of the \(c\)-\textit{numerical ranges} of differential operators ⋮ The Perron eigenspace of nonnegative almost skew-symmetric matrices and Levinger's transformation

Cites Work

• Unnamed Item
• Unnamed Item
• G-invariant norms and G(c)-radii
• The constrained bilinear form and the C-numerical range
• Duality between some linear preserver problems. II: Isometries with respect to c-spectral norms and matrices with fixed singular values
• Elementary inclusion relations for generalized numerical ranges
• Constrained extrema of bilinear functionals
• Norm properties of C-numerical radii
• The invarianee ofC-numerical rangeC-numericai radius, and their dual problems
• TheC-convex matrices
• Linear operators that preserve thec-numerical range or radius of matrices
• Duality between some linear preservers problems: the invariance of thec-numerical range, thec-numerical radius and certain matrix sets
• Inequalities relating norms invariant under unitary similarities
• Rigid Embedding of Simple Groups in the General Linear Group
• Invariants of linear maps on matrix algebras

This page was built for publication: A generalized numerical range: the range of a constrained sesquilinear form