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On the generalized numerical range

โœ Scribed by Fan, M. K. H.; L Tits, A.


Book ID
120991351
Publisher
Taylor and Francis Group
Year
1987
Tongue
English
Weight
508 KB
Volume
21
Category
Article
ISSN
0308-1087

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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.

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Suppose m and n are integers such that 1 m n, and H is a subgroup of the symmetric group S m of degree m. Define the generalized matrix function associated with the principal character of the group H on an m ร— m matrix B = (b ij ) by b jฯƒ (j) , and define the generalized numerical range of an n ร— n