SOME PROPERTIES OF NORMAL OPERATORS

In this paper, we investigate the conditions under which a normal operator is bounded. It is known that, if T is self-adjoint and ¾(T) is bounded, then T is bounded. We try to extend this for normal operators. And, we prove that the Moor- Penrose inverse of a normal operator is normal. Also, we prove that the approximate point spectrum of normal operator T equals to the spectrum of T.