Results 11 to 20 of about 489,763 (264)
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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Some Results on Polynomial Numerical Hulls of Perturbed Matrices [PDF]
Sahand Communications in Mathematical Analysis, 2019 In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.
Madjid Khakshour, Gholamreza Aghamollaei
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THE SPECTRAL SCALE AND THE NUMERICAL RANGE [PDF]
International Journal of Mathematics, 2003 Suppose that c is an operator on a Hilbert Space H such that the von Neumann algebra N generated by c is finite. Let τ be a faithful normal tracial state on N and set b1= (c + c*)/2 and b2= (c - c*)/2i. Also write B for the spectral scale of {b1, b2} relative to τ. In previous work by the present authors, some joint with Nik Weaver, B has been shown to
Akemann, Charles A., Anderson, Joel
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Investigations of the numerical range of a operator matrix
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 We consider a $2\times2$ operator matrix $A$ (so-called generalized Friedrichs model) associated with a system of at most two quantum particles on ${\rm d}$-dimensional lattice.
Tulkin Kh Rasulov, Elyor B Dilmurodov
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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 Range of Moore–Penrose Inverse Matrices
Mathematics, 2020 Let A be an n-by-n matrix. The numerical range of A is defined as W ( A ) = { x * A x : x ∈ C n , x * x = 1 } . The Moore–Penrose inverse A + of A is the unique matrix satisfying A A + A = A , A + A A + = A ...
Mao-Ting Chien
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On partial isometries with circular numerical range
Concrete Operators, 2021 In their LAMA 2016 paper Gau, Wang and Wu conjectured that a partial isometry A acting on ℂn cannot have a circular numerical range with a non-zero center, and proved this conjecture for n ≤ 4. We prove it for operators with rank A = n − 1 and any n.
Wegert Elias, Spitkovsky Ilya
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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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Spatial numerical ranges of elements of subalgebras of C0(X)
International Journal of Mathematics and Mathematical Sciences, 2000 When A is a subalgebra of the commutative Banach algebra C0(X) of all continuous complex-valued functions on a locally compact Hausdorff space X, the spatial numerical range of element of A can be described in terms of positive measures.
Sin-Ei Takahasi
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On Preserving Properties of Linear Maps on $C^{*}$-algebras [PDF]
Sahand Communications in Mathematical Analysis, 2020 Let $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation.
Fatemeh Golfarshchi +1 more
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