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Joint numerical ranges: recent advances and applications minicourse by V. Müller and Yu. Tomilov
Concrete Operators, 2020 We present a survey of some recent results concerning joint numerical ranges of n-tuples of Hilbert space operators, accompanied with several new observations and remarks.
Müller V., Tomilov Yu.
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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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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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Volterra operator norms : a brief survey
Moroccan Journal of Pure and Applied Analysis, 2023 In this expository article, we discuss the evaluation and estimation of the operator norms of various functions of the Volterra operator.
Ransford Thomas
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The numerical range of derivations
Linear Algebra and its Applications, 1989 AbstractLet p, q, n be integers satisfying 1 ⩽ p ⩽ q ⩽ n. The (p, q)-numerical range of an n×n complex matrix A is defined by Wp,q(A) = {Ep((UAU∗)[q]): U unitary}, where for an n×n complex matrix X, X[q] denotes its q×q leading principal submatrix and Ep(X[q]) denotes the pth elementary symmetric function of the eigenvalues of X[q]. When 1 = p = q, the
Li, CK, Tsing, NK
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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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On different definitions of numerical range [PDF]
J. Math. Anal. Appl. 433 (2016), 877-866, 2015 We study the relation between the intrinsic and the spatial numerical ranges with the recently introduced "approximated" spatial numerical range. As main result, we show that the intrinsic numerical range always coincides with the convex hull of the approximated spatial numerical range. Besides, we show sufficient conditions and necessary conditions to
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Higher Rank Numerical Ranges of Normal Operators and unitary dilations [PDF]
J. Math. Anal. Appl. (2023), 2021 We describe here the higher rank numerical range, as defined by Choi, Kribs and Zyczkowski, of a normal operator on an infinite dimensional Hilbert space in terms of its spectral measure. This generalizes a result of Avendano for self-adjoint operators.
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Reduction of the c-numerical range to the classical numerical range
Linear Algebra and its Applications, 2011 AbstractLet A be an n×n complex matrix and c=(c1,c2,…,cn) a real n-tuple. The c-numerical range of A is defined as the setWc(A)=∑j=1ncjxj∗Axj:{x1,x2,…,xn}isanorthonormalbasisforCn.When c=(1,0,…,0), Wc(A) becomes the classical numerical range of A which is often defined as the setW(A)={x∗Ax:x∈Cn,x∗x=1}.We show that for any n×n complex matrix A and real ...
Mao-Ting Chien, Hiroshi Nakazato
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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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