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In this paper, we introduce a new type of Drazin invertible operator on Hilbert spaces, which is called D-operator. Then, some properties of the class of Doperators are studied. We prove that the D-operator preserves the scalar product, the unitary equivalent property, the product and sum of two D-operators are not D-operator in general but the direct product and tenser product is also D-operator. [ABSTRACT FROM AUTHOR]

In this paper we characterize self-adjoint and normal composition operators on Poisson weighted sequence spaces l²(λ). However, the main purpose of this paper is to determine explicit conditions on inducing map under which a composition operator admits a best normal approximation. We extend results of Tripathi and Lal [Antinormal composition operators on l², Tamkang J. Math. 39 (2008), 347-352] to characterize antinormal composition operators on l²(λ). [ABSTRACT FROM AUTHOR]

Abstract: We introduce the spectral points of two-sided positive type of bounded normal operators in Krein spaces. It is shown that a normal operator has a local spectral function on sets which are of two-sided positive type. In addition, we prove that the Riesz–Dunford spectral subspace corresponding to a spectral set which is only of positive type is uniformly positive. The restriction of the operator to this subspace is then normal in a Hilbert space. [Copyright &y& Elsevier]

Abstract: Let be the -algebra of all bounded linear operators acting on a complex Hilbert space H. In this note, we shall show that if S is an invertible normal operator in the following estimation holds where is the injective norm on the tensor product . This last inequality becomes an equality when S is invertible self-adjoint. On the other hand, we shall characterize the set of all invertible normal operators S in satisfying the relation and also we shall give some characterizations of some subclasses of normal operators in by inequalities or equalities. [Copyright &y& Elsevier]

Abstract: This paper is concerned with operators on Hilbert space of the form where D is a diagonalizable normal operator and is a rank-one operator. It is shown that if and the vectors u and v have Fourier coefficients and with respect to an orthonormal basis that diagonalizes D that satisfy , then T has a nontrivial hyperinvariant subspace. This partially answers an open question of at least 30 years duration. [Copyright &y& Elsevier]