The q-numerical range and the Davis-Wielandt shell of reducible 3 × 3 matrices

Chien, M-T; Nakazato, H; Psarrakos, P

dc.contributor.author	Chien, M-T	en
dc.contributor.author	Nakazato, H	en
dc.contributor.author	Psarrakos, P	en
dc.date.accessioned	2014-03-01T01:25:16Z
dc.date.available	2014-03-01T01:25:16Z
dc.date.issued	2006	en
dc.identifier.issn	0308-1087	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17627
dc.subject	Cone	en
dc.subject	Davis-Wielandt shell	en
dc.subject	Ellipsoid	en
dc.subject	q-Numerical range	en
dc.subject.classification	Mathematics	en
dc.subject.other	HILBERT-SPACE OPERATOR	en
dc.subject.other	POLYNOMIALS	en
dc.title	The q-numerical range and the Davis-Wielandt shell of reducible 3 × 3 matrices	en
heal.type	journalArticle	en
heal.identifier.primary	10.1080/00036810500148994	en
heal.identifier.secondary	http://dx.doi.org/10.1080/00036810500148994	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	For a given q is an element of [0, 1], the q-numerical range of an n x n complex matrix A is defined by F-q(A) = {x* Ay is an element of C : x, y is an element of C-n, x* x = y* y = 1, x* y = q}, and it is closely related with the Davis-Wielandt shell of A, W(A, A* A) = {(x* Ax, x* A* Ax) is an element of C x R : x is an element of C-n, x* x = 1}. In this article, we investigate systematically the q-numerical range of the 3 x 3 matrix [GRAPHICS] and obtain the equation of its boundary by taking advantage of the special shape of W(A(alpha), A(alpha)* A(alpha)). Furthermore, a parametric representation of partial derivative F-q(A(alpha)) and the construction of a 4 x 4 matrix B-q such that F-q(A(alpha)) = F-1(B-q) are discussed. The q-numerical range of a certain normal operator on an infinite Hilbert space of complex-valued (Lebesgue) measurable functions is also considered.	en
heal.publisher	TAYLOR & FRANCIS LTD	en
heal.journalName	Linear and Multilinear Algebra	en
dc.identifier.doi	10.1080/00036810500148994	en
dc.identifier.isi	ISI:000234137700001	en
dc.identifier.volume	54	en
dc.identifier.issue	2	en
dc.identifier.spage	79	en
dc.identifier.epage	112	en