Numerical radius and distance from unitary operators
Cătălin Badea, Michel Crouzeix · Operators and Matrices · 2013
Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that w(A) 1+ and w(A -1 ) 1+ for some 0 . It is shown that inf{ A-U : U unitary } c 1/4 for some constant c > 0 . This generalizes a result due to J.G. Stampfli, which is obtained for = 0 . An example is given showing that the exponent 1/4 is optimal. The more general case of the operator -radius w () is discussed for 1 2 .