A SURVEY ON LINEAR PRESERVERS OF NUMERICAL RANGES AND RADII
Chi-Kwong Li · 2001
We survey results on linear operators leaving invariant different kinds of generalized numerical ranges and numerical radii. Keywords: Linear operator, numerical range (radius). 1991 AMS Subject Classification: 15A04, 15A60, 47B49 1 Introduction Let B(H) be the algebra of bounded linear operators acting on the Hilbert space H. If dimH = n, we identify B(H) with M n , the algebra of n \\Theta n complex matrices. The numerical range (or field of values) of A 2 B(H) is the set W (A) = f(Ax; x) : x 2 H; (x; x) = 1g; and the numerical radius of A is the quantity r(A) = supfjzj : z 2 W (A)g: The study of numerical range and numerical radius has a long history (see [8, Chapter 1] and its references). There are many generalizations of these concepts motivated by both theoretical study and applications. A keyword search in MathSciNet will generate hundreds of items. These papers are related to many different subjects in pure and applied sciences. Among the many directions of active resea...