On numerical range of the Aluthge transformation Original Research Article

Let T=UT be the polar decomposition of an operator T. Aluthge defined an operator transformation image of T which is called Aluthge transformation. In this paper, we shall discuss the numerical range of image , and show the following results: 1. (i) image . 2. (ii) If T is an n×n matrix, then image . 3. (iii) If N(T)subset ofN(T*), then image . Moreover, we shall obtain some applications of above results.