Related papers: Products of Unbounded Normal Operators

The purpose of this paper is to generalize a very famous result on products of normal operators, due to I. Kaplansky. The context of generalization is that of bounded hyponormal and unbounded normal operators on complex separable Hilbert…

Let $A$ and $B$ be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.

In the present paper, we generalized some notions of bounded operators to un- bounded operators on Hilbert space such as k-quasihyponormal and k-paranormal unbounded operators. Furthermore, we extend the Kaplansky theorem for normal…

Let $A$ and $B$ be two densely defined unbounded closeable operators in a Hilbert space such that their unbounded operator products $AB$ and $BA$ are also densely defined. Then all four operators possess adjoints and we obtain new inclusion…

This paper is a continuation of the paper (A.G.Ramm, Amer. Math. Monthly, 108, N 9, (2001), 855-860), where bounded Fredholm operators are studied. The theory of bounded linear Fredholm-type operators is presented in many texts. This paper…

Normality of bounded and unbounded adjointable operators are discussed. Suppose $T$ is an adjointable operator between Hilbert C*-modules which has polar decomposition, then $T$ is normal if and only if there exists a unitary operator $…

In this article, we proved upper bounds for numerical radius of bounded linear operator and product of operators which generalize and improve existing inequalities. We also obtain a numerical radius inequality of invertible operator using…

Various characterizations of unbounded closed densely defined operators commuting with the spectral measures of their moduli are established.In particular, Kaufman's definition of an unbounded quasinormal operator is shown to coincide with…

An acute look at \underbar{basic} facts concerning \underbar{unbounded} subnormal operators is taken here. These operators have the richest structure and are the most exciting among the whole family of beneficiaries of the normal ones.…

The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of those normal operators are given. This is carried out without the known $2\pi i$-congruence-free…

A new proof following a suggestion of Kaplansky to use a result of Dixmier, and in this way avoid unbounded nets of operators, is given of the Kaplansky density theorem.

Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.

Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.

The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this…

We introduce and study the class of unbounded DunfordPettis operators. As consequences, we give basic properties and derive interesting results about the duality, domination problem and relationship with other known classes of operators.

In the present paper we give results on the closedness and the self-adjointness of the sum of two unbounded operators. We present a new approach to these fundamental questions in operator theory. We also prove a new version of the Fuglede…

In this note basic properties of unbounded weighted conditional expectation operators are investigated. A description of polar decomposition and quasinormality in this context are provided. Also, we study hyperexpan- sive weighted…

The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…

Bounded and unbounded weighted composition operators on $L^2$ spaces over $\sigma$-finite measure spaces are investigated. A variety of questions related to seminormality of such operators are discussed.

In this paper we give and prove a criterion for the normality of unbounded closed operators, which is a sort of a maximality result which will be called "double maximality". As applications, we show, under some assumptions, that the sum of…