Maps preserving the joint numerical radius distance of operators

Abstract

Dedicated to Professor David Lutzer on the occasion of his retirement. AbstractDenote the joint numerical radius of an m-tuple of bounded operators A = (A 1 , . . . , A m ) by w(A). We give a complete description of maps f satisfying w(A − B) = w(f (A) − f (B)) for any two m-tuples of operators A = (A 1 , . . . , A m ) and B = (B 1 , . . . , B m ). We also characterize linear isometries for the joint numerical radius, and maps preserving the joint numerical range of A.

MAPPING PRESERVING NUMERICAL RANGE OF OPERATOR PRODUCTS ON C*-ALGEBRAS

“…In the last few decades, there has been a considerable interest in the problem of characterization of maps that preserves the numerical range or the numerical radius, see for instance the papers [4,12,13,15] and the references therein. Notice that, based on the aforesaid, preserving the usual numerical range W implies the preservation of the spacial numerical range V .…”