Results 1 to 10 of about 463,320 (265)
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, Tretter, Christiane
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On joint numerical ranges [PDF]
Pacific Journal of Mathematics, 1978 The joint numerical status of commuting bounded operators Ai and A2 on a Hubert space is defined as {{φiA^y φ(A2)) such that φ is a state on the C*-algebra generated by Ax and A2}. It is shown that if At and A2 are commuting normal operators then their joint numerical status equals the closure of their joint numerical range.
Buoni, John J., Wadhwa, Bhushan L.
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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.
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On generalized numerical ranges [PDF]
Pacific Journal of Mathematics, 1976 which ||(T- viyι\\ = l/d(υ, W(T)), v£ CLW(T), where CLW(T) is the closure of the numerical range W(T) of Γ, has been generalized by using the concept of generalized numerical ranges due to C. S. Lin. Also it has been shown that the notions of generalized Minkowski distance functionals and generalized numerical ranges arise in a natural way for elements
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Polynomials and Numerical Ranges [PDF]
Proceedings of the American Mathematical Society, 1988 Let A A be an n × n n \times n complex matrix. For 1 ≤ k ≤ n 1 \leq k \leq n we study the inclusion relation for the following polynomial sets related to the matrix A A . (a) The classical numerical range of the k
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Reduction of the c-numerical range to the classical numerical range
Linear Algebra and its Applications, 2011 For an \(n\)-by-\(n\) complex matrix \(A\) and a real \(n\)-tuple \(c=(c_1,\dots, c_n)\), the \(c\)-numerical range \(W_c(A)\) of \(A\) is, by definition, the subset \[ \Biggl\{\sum^n_{j=1} c_j x^*_j Ax_j: x_1,\dots, x_n\text{ form an orthonormal basis of }\mathbb{C}^n\Biggr\} \] of the complex plane.
Chien, Mao-Ting, Nakazato, Hiroshi
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Numerical ranges of KMS matrices [PDF]
Acta Scientiarum Mathematicarum, 2013 A KMS matrix is one of the form $$J_n(a)=[{array}{ccccc} 0 & a & a^2 &... & a^{n-1} & 0 & a & \ddots & \vdots & & \ddots & \ddots & a^2 & & & \ddots & a 0 & & & & 0{array}]$$ for $n\ge 1$ and $a$ in $\mathbb{C}$.
Gau, Hwa-Long, Wu, Pei Yuan
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H-joint numerical ranges [PDF]
Bulletin of the Australian Mathematical Society, 2002 The notion of the joint numerical range of several linear operators with respect to a sesquilinear form is introduced. Geometrical properties of the joint numerical range are studied, in particular, convexity and angle points, in connection with the algebraic properties of the operators. The main focus is on the finite dimensional case.
Li, Chi-Kwong, Rodman, Leiba
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Numerical Range and Quadratic Numerical Range for Damped Systems
, 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
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Linear Algebra and its Applications, 2015 Let \(H\) be a separable complex Hilbert space and let \(B(H)\) be the Banach algebra of all bounded linear operators on \(H\). The numerical range of \(S\in B(H)\) is the set \(W(S)=\left\{(Sx,x):\; ||x||\; =1\right\}\). It is known that the spectrum \(\sigma (S)\) of \(S\) is contained in \(W(S)\). In this paper, the authors define a more general set,
Bracic, J., Diogo, C.
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