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On operators Cauchy dual to 2-hyperexpansive operators: the unbounded case

Sameer Chavan (2011)

Studia Mathematica

The Cauchy dual operator T’, given by T ( T * T ) - 1 , provides a bounded unitary invariant for a closed left-invertible T. Hence, in some special cases, problems in the theory of unbounded Hilbert space operators can be related to similar problems in the theory of bounded Hilbert space operators. In particular, for a closed expansive T with finite-dimensional cokernel, it is shown that T admits the Cowen-Douglas decomposition if and only if T’ admits the Wold-type decomposition (see Definitions 1.1 and 1.2 below)....

On operators close to isometries

Sameer Chavan (2008)

Studia Mathematica

We introduce and discuss a class of operators, to be referred to as operators close to isometries. The Bergman-type operators, 2-hyperexpansions, expansive p-isometries, and certain alternating hyperexpansions are main examples of such operators. We establish a few decomposition theorems for operators close to isometries. Applications are given to the theory of p-isometries and of hyperexpansive operators.

On the Range and the Kernel of Derivations

Bouali, Said, Bouhafsi, Youssef (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.Let H be a separable infinite dimensional complex Hilbert space and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A ∈ L(H), the derivation δA : L(H)→ L(H) is defined by δA(X) = AX-XA. In this paper we prove that if A is an n-multicyclic hyponormal operator and T is hyponormal such that AT = TA, then || δA(X)+T|| ≥ ||T|| for all X ∈ L(H). We establish the same inequality if A is...

On the range-kernel orthogonality of elementary operators

Said Bouali, Youssef Bouhafsi (2015)

Mathematica Bohemica

Let L ( H ) denote the algebra of operators on a complex infinite dimensional Hilbert space H . For A , B ∈ L ( H ) , the generalized derivation δ A , B and the elementary operator Δ A , B are defined by δ A , B ( X ) = A X - X B and Δ A , B ( X ) = A X B - X for all X ∈ L ( H ) . In this paper, we exhibit pairs ( A , B ) of operators such that the range-kernel orthogonality of δ A , B holds for the usual operator norm. We generalize some recent results. We also establish some theorems on the orthogonality of the range and the kernel of Δ A , B with respect to the wider class of unitarily invariant norms on...

On the Φ class operators.

Bachir, A., Segres, A. (2009)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

On totally * -paranormal operators

Eungil Ko, Hae-Won Nam, Young Oh Yang (2006)

Czechoslovak Mathematical Journal

In this paper we study some properties of a totally * -paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally * -paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally * -paranormal operators through the local spectral theory. Finally, we show that every totally * -paranormal operator satisfies an analogue of the single valued extension property for W 2 ( D , H ) and some of totally * -paranormal operators have scalar extensions....

On unbounded hyponormal operators III

J. Janas (1994)

Studia Mathematica

The paper deals mostly with spectral properties of unbounded hyponormal operators. Some nontrivial examples of such operators are given.

On w-hyponormal operators

Eungil Ko (2003)

Studia Mathematica

We study some properties of w-hyponormal operators. In particular we show that some w-hyponormal operators are subscalar. Also we state some theorems on invariant subspaces of w-hyponormal operators.

Operator equations and subscalarity

Sungeun Jung, Eungil Ko (2014)

Studia Mathematica

We consider the system of operator equations ABA = A² and BAB = B². Let (A,B) be a solution to this system. We give several connections among the operators A, B, AB, and BA. We first prove that A is subscalar of finite order if and only if B is, which is equivalent to the subscalarity of AB or BA with finite order. As a corollary, if A is subscalar and its spectrum has nonempty interior, then B has a nontrivial invariant subspace. We also provide examples of subscalar operator matrices. Moreover,...

Currently displaying 81 – 100 of 167