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Linear maps transforming the higher numerical ranges

โœ Scribed by Chi-Kwong Li; Yiu-Tung Poon; Nung-Sing Sze

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
321 KB
Volume
400
Category
Article
ISSN
0024-3795

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Let M n be the semigroup of n ร— n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in M n including the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose ฮ› k (A) is the rank-k numerical range

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In this paper the authors show that the Aluthge transformation T of a matrix T and a polynomial f satisfy the inclusion relation W C (f ( T )) โŠ‚ W C (f (T )) for the generalized numerical range if C is a Hermitian matrix or a rank-one matrix.

Differential properties of the numerical
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Let A = (A,, A,) be a pair of Hermitian operators in @" and A = A, + iA,. We investigate certain differential properties of the numerical range map nA: r H )) with the aim of better understanding the nature of the numerical range W(A) of A. For example, the joint eigenvalues of A correspond to the s