Title: On the range kernel orthogonality and p-symmetric operators
Abstract: Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra of all bounded linear operators on H .For given A ∈ L(H) , we define the derivation δ A : L(H) -→ L(H) by δ A (X) = AX -XA .In this paper we establish the orthogonality of the range R(δ A ) and the kernel ker(δ A ) of a derivation δ A induced by a cyclic subnormal operator A , in the usual sense.We give a version of the Putnam -Fuglede theorem.We establish a short proof of the principal result of F. Wenying and J. Guoxing in [10].Relatad results for P-symmetric operators are also given.