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The numerical range and decomposable numerical range of matrices
Linear and Multilinear Algebra, 1991Let m and n be positive integers such that 1≤m≤n. Denote by the set of all n×m complex matrices. For a matrix , the mth decomposable numerical range of A is the set When m=1, it reduces to the classical numerical range of A which is denoted by W(A). It is known that is contaned in W(Cm (A)), where Cm (A) is the mth compound of A. In this paper we study
Natália Bebiano +2 more
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Numerical range submultiplicity
Linear and Multilinear Algebra, 2015Let and be elements of a complex unital Banach algebra. The numerical range submultiplicity is investigated. As a consequence of the inclusions established, we confirm a conjecture that if and are self-adjoint operators such that is positive then the product is self-adjoint whenever it is normal.
Mohamed Barraa, Mohamed Boumazgour
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Ratio Numerical Ranges of Operators
Integral Equations and Operator Theory, 2011Let \(H\) be a Hilbert space and \(L(H)\) the algebra of bounded linear operators on \(H\). For \(A\in L(H)\), the numerical range of \(A\) is given by \(W(A)= \{\langle Ax,x\rangle:x\in H,\;\langle x,x\rangle=1\}\). For \(A,B\in L(H)\), \(B\neq 0\), define the ratio numerical range \[ W(A/B)=\left\{\frac{\langle Ax,x\rangle}{\langle Bx,x\rangle}:x\in ...
Rodman, Leiba, Spitkovsky, Ilya M.
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1973
Numerical Ranges II is a sequel to Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by the same authors and published in this series in 1971. The present volume reflects the progress made in the subject, expanding and discussing topics under the general headings of spatial and algebra numerical ranges and ...
F. F. Bonsall, J. Duncan
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Numerical Ranges II is a sequel to Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by the same authors and published in this series in 1971. The present volume reflects the progress made in the subject, expanding and discussing topics under the general headings of spatial and algebra numerical ranges and ...
F. F. Bonsall, J. Duncan
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Numerical Range of Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications, 1994Let \(A_ i\), \(i = 1, \dots, m\) be \(n \times n\) matrices with complex coefficients and consider the matrix polynomial \(P(\lambda) = \sum_{i=0}^ m A_ i \lambda^ i\). The numerical range of \(P(\lambda)\) is defined through \[ W \bigl( P(\lambda) \bigr) : = \{\mu \in \mathbb{C} \mid x^* P(\mu)x = 0 \quad \text{for some nonzero} \quad x \in \mathbb{C}
Li, Chi-Kwong, Rodman, Leiba
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Essential numerical range and maximal numerical range of the Aluthge transform
Linear and Multilinear Algebra, 2007Let T be a bounded linear operator on a complex separable Hilbert space . Let and be the Aluthge transform and *-Aluthge transform of T respectively. In this article, we consider the essential numerical range and maximal numerical range of T, and . We prove that the essential numerical range of is always contained in that of T and is the same as that ...
Guoxing Ji, Ni Liu, Ze Li
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Generalized higher-rank numerical range
2012Summary: In this note, a generalization of higher rank numerical range is introduced and some of its properties are investigated.
AFSHIN, HAMID REZA +2 more
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The evolving landscape of salivary gland tumors
Ca-A Cancer Journal for Clinicians, 2023Conor Steuer
exaly