Results 11 to 20 of about 419,543 (296)
On the numerical range of an operator [PDF]
Proceedings of the American Mathematical Society, 1963 The numerical range of an operator P in a Hubert space is defined as the set of all the complex numbers (Tx, x), where x is a unit vector in the space. It is well known that a bounded normal operator has the property that the closure of its numerical range is exactly the convex hull of its spectrum [5, pp. 325-327, Theorem 8.13 and Theorem 8.14].
Ching-Hwa Meng
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On the geometry of numerical ranges [PDF]
Pacific Journal of Mathematics, 1975 M. Radjabalipour, Heydar Radjavi
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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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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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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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