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ON THE RANGE OF THE MAP N AB | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 49, Issue 2, 2008, Pages 158-161 | ||
| Author | ||
| Sadiq Naji Nassir | ||
| Abstract | ||
| Let H be an infinite dimensional separable complex Hilbert space and B(H) be the Banach algebra of all bounded linear operators on H. In this paper we introduce a mapping : B(H) → B(H) . By (T)=AT-T*B , T B(H). ABNABN We study some properties of it , and we study surjectivity of this mapping when A is pseudonormal operator whose spectrum satisfies certain properties if the analytic function f(A) that belongs to the *AARangeN then f(A) is the zero function .Also we generalize some results for the Jordan * derivation and the derivatio | ||
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