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Numerical range of s(φ)

- Hwa-Long Gau, Pei Yuan Wu
- Mathematics
- 1 November 1998

We make a detailed study of the numerical ranges W(T) of completely nonunitary contractions T with the property rank (1-T∗T)=1 on a finite-dimensional Hilbert space. We show that such operators are… Expand

NUMERICAL RANGE AND PONCELET PROPERTY

- Hwa-Long Gau, Pei Yuan Wu
- Mathematics
- 6 January 2003

In this survey article, we give an expository account of the recent developments on the Poncelet property for numerical ranges of the compressions of the shift $S(\phi)$. It can be considered as an… Expand

Condition for the numerical range to contain an elliptic disc

- Hwa-Long Gau, Pei Yuan Wu
- Mathematics
- 1 May 2003

For an n-by-n matrix A and an elliptic disc E in the plane, we show that the sum of the number of common supporting lines and the number of common intersection points to E and the numerical range W(… Expand

HIGHER-RANK NUMERICAL RANGES AND DILATIONS

- Hwa-Long Gau, Chi-Kwong Li, Pei Yuan Wu
- Mathematics
- 1 December 2010

For any n-by-n complex matrix A and any k, 1 ≤ k ≤ n, let Λk(A) = {λ ∈ C : X∗AX = λIk for some n-by-k X satisfying X∗X = Ik} be its rank-k numerical range. It is shown that if A is an n-by-n… Expand

Anderson’s theorem for compact operators

- Hwa-Long Gau, Pei Yuan Wu
- Mathematics
- 5 June 2006

It is shown that if A is a compact operator on a Hilbert space with its numerical range W(A) contained in the closed unit disc D and with W(A) intersecting the unit circle at infinitely many points,… Expand

Numerical Ranges of KMS Matrices

- Hwa-Long Gau, Pei Yuan Wu
- Mathematics
- 1 April 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… Expand

Companion matrices: reducibility, numerical ranges and similarity to contractions

- Hwa-Long Gau, Pei Yuan Wu
- Mathematics
- 15 May 2004

Abstract In this paper, we study some unitary-equivalence properties of the companion matrices. We obtain a criterion for a companion matrix to be reducible and show that the numerical range of a… Expand

Lucas' theorem refined ∗

- Hwa-Long Gau, Pei Yuan Wu
- Mathematics
- 1 April 1999

We prove a refined version of the classical Lucas' theorem: if p is a polynomial with zeros a 1,…,a n+1 all having modulus one and φis the Blaschke product whose zeros are those of the derivative p… Expand

Numerical range circumscribed by two polygons

- Hwa-Long Gau, Pei Yuan Wu
- Mathematics
- 1 May 2004

Abstract We show that, for any 2 n +2 distinct points a 1 , a 1 ′ , a 2 , a 2 ′ ,…, a n +1 , a n +1 ′ (in this order) on the unit circle, there is an n -by- n matrix A , unique up to unitary… Expand

Numerical Range of a Normal Compression

- Hwa-Long Gau, Pei Yuan Wu †
- Mathematics
- 1 May 2004

Let N be an n-by-n diagonal matrix whose distinct eigenvalues form corners of their convex hull, let x be a vector in with nonzero components, and let A be the compression of N to the orthogonal… Expand

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