Lambda-Aluthge transforms and Schatten ideals

ANTEZANA, JORGE; MASSEY, PEDRO; STOJANOFF, DEMETRIO

LINEAR ALGEBRA AND ITS APPLICATIONS

ELSEVIER

Año: 2005 vol. 405 p. 177 - 199

0024-3795

Let TÎ L(H) and let T=U½ T½ = ½ T*½ U be the polar decomposition of T . Then, for every l Î [0,1], the l -Aluthge transform is defined by D l (T )= ½ T½ l U½ T½ 1-l . We show that several properties which are known for the usual Aluthge transform (i.e. the case l =1 2) also hold for l -Aluthge transforms with l Î (0,1) . Moreover, we get several results which are new, even for the usual Aluthge transform.