scholarly journals Joint numerical range and its generating hypersurface

2010 ◽  
Vol 432 (1) ◽  
pp. 173-179 ◽  
Author(s):  
Mao-Ting Chien ◽  
Hiroshi Nakazato
Keyword(s):  
Numerical Range ◽  
Joint Numerical Range

scholarly journals SPECTRUM, NUMERICAL RANGE AND DAVIS-WIELANDT SHELL OF A NORMAL OPERATOR

2009 ◽  
Vol 51 (1) ◽  
pp. 91-100 ◽  
Author(s):  
CHI-KWONG LI ◽  
YIU-TUNG POON
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Convex Set ◽  
Numerical Range ◽  
Normal Operator ◽  
Additional Information ◽  
Commuting Operators ◽  
Boundary Points ◽  
Reducing Subspace ◽  
Joint Numerical Range

AbstractWe denote the numerical range of the normal operator T by W(T). A characterization is given to the points in W(T) that lie on the boundary. The collection of such boundary points together with the interior of the the convex hull of the spectrum of T will then be the set W(T). Moreover, it is shown that such boundary points reveal a lot of information about the normal operator. For instance, such a boundary point always associates with an invariant (reducing) subspace of the normal operator. It follows that a normal operator acting on a separable Hilbert space cannot have a closed strictly convex set as its numerical range. Similar results are obtained for the Davis-Wielandt shell of a normal operator. One can deduce additional information of the normal operator by studying the boundary of its Davis-Wielandt shell. Further extension of the result to the joint numerical range of commuting operators is discussed.

scholarly journals Convexity of the joint numerical range: topological and differential geometric viewpoints

2004 ◽  
Vol 376 ◽  
pp. 143-171 ◽  
Author(s):  
Eugene Gutkin ◽  
Edmond A. Jonckheere ◽  
Michael Karow
Keyword(s):  
Numerical Range ◽  
Joint Numerical Range

A note on the convexity of the indefinite joint numerical range

2014 ◽  
Vol 27 ◽  
Author(s):  
Hiroshi Nakazato ◽  
Natalia Bebiano ◽  
Joao Da Providencia
Keyword(s):  
Numerical Range ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Hermitian Matrices ◽  
Krein Spaces ◽  
Necessary And Sufficient ◽  
Joint Numerical Range

This note investigates the convexity of the indefinite joint numerical range of a tuple of Hermitian matrices in the setting of Krein spaces. Its main result is a necessary and sufficient condition for convexity of this set. A new notion of “quasi-convexity” is introduced as a refinement of pseudo-convexity.

Convexity of the Joint Numerical Range

2000 ◽  
Vol 21 (2) ◽  
pp. 668-678 ◽  
Author(s):  
Chi-Kwong Li ◽  
Yiu-Tung Poon
Keyword(s):  
Numerical Range ◽  
Joint Numerical Range

scholarly journals H-joint numerical ranges

2002 ◽  
Vol 66 (1) ◽  
pp. 105-117
Author(s):  
Chi-Kwong Li ◽  
Leiba Rodman
Keyword(s):  
Numerical Range ◽  
Linear Operators ◽  
Dimensional Case ◽  
Geometrical Properties ◽  
Finite Dimensional ◽  
Sesquilinear Form ◽  
Algebraic Properties ◽  
Finite Dimensional Case ◽  
Joint Numerical Range

The notion of the joint numerical range of several linear operators with respect to a sesquilinear form is introduced. Geometrical properties of the joint numerical range are studied, in particular, convexity and angle points, in connection with the algebraic properties of the operators. The main focus is on the finite dimensional case.

Sign in / Sign up

Export Citation Format

Share Document