Numerical Radius Isometries

Authors: Li C-K.1; Scaronemrl P.2

Source: Linear and Multilinear Algebra, Volume 50, Number 4, 1 January 2002 , pp. 307-314(8)

Publisher: Taylor and Francis Ltd

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Abstract:

Let V be a direct sum of full matrix algebras, or the algebra of block upper triangular matrices. Suppose r(A) is the numerical radius of $A in V$. We characterize mappings $f: V rightarrow V$ that satisfy $r(;f(A)-f(B)) = r(A-B) {rm for all} A, B in V$.

Keywords: Isometry; Linear operator; Numerical range; Numerical radius

Document Type: Research article

Affiliations: 1: Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795, USA 2: Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

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