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Numerical ranges of weighted shift matrices

โœ Scribed by Ming Cheng Tsai; Pei Yuan Wu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
250 KB
Volume
435
Category
Article
ISSN
0024-3795

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๐Ÿ“œ SIMILAR VOLUMES

The -numerical range of 3-by-3 weighted
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โœ Mao-Ting Chien; Hiroshi Nakazato ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 189 KB

Let A be a 3-by-3 weighted shift matrix with weights {s 1 , s 2 }. The q-numerical radius of A is found as an implicit function in q, s 1 , s 2 .

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We show that an n-by-n companion matrix A can have at most n line segments on the boundary NW (A) of its numerical range W(A), and it has exactly n line segments on NW (A) if and only if, for n odd, A is unitary, and, for n even, A is unitarily equivalent to the direct sum A 1 โŠ• A 2 of two (n/2)-by-

Numerical ranges of large Toeplitz matri
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โœ Steffen Roch ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 739 KB

A Banach algebraic approach is proposed to study the asymptotic bchaviour of the numerical ranges of certain (finite) approximation matrices of {infinite) operators. The approach works for large classes of approximation methods; it is examined in detail here for the finite sections of Toeplitz opera