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Displaying similar documents to “On the Range and the Kernel of Derivations”

Trace formulae for p-hyponormal operators

Muneo Chō, Tadasi Huruya (2004)

Studia Mathematica

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The purpose of this paper is to introduce mosaics and principal functions of p-hyponormal operators and give a trace formula. Also we introduce p-nearly normal operators and give trace formulae for them.

Generalized D-Symmetric Operators I

Bouali, S., Ech-chad, M. (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30. Let H be an infinite-dimensional complex Hilbert space and let A, B ∈ L(H), where L(H) is the algebra of operators on H into itself. Let δAB: L(H) → L(H) denote the generalized derivation δAB(X) = AX − XB. This note will initiate a study on the class of pairs (A,B) such that [‾(R(δAB))] = [‾(R(δB*A*))]; i.e. [‾(R(δAB))] is self-adjoint.

Fuglede-Putnam theorem for class A operators

Salah Mecheri (2015)

Colloquium Mathematicae

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Let A ∈ B(H) and B ∈ B(K). We say that A and B satisfy the Fuglede-Putnam theorem if AX = XB for some X ∈ B(K,H) implies A*X = XB*. Patel et al. (2006) showed that the Fuglede-Putnam theorem holds for class A(s,t) operators with s + t < 1 and they mentioned that the case s = t = 1 is still an open problem. In the present article we give a partial positive answer to this problem. We show that if A ∈ B(H) is a class A operator with reducing kernel and B* ∈ B(K) is a class 𝓨 operator,...

Backward Aluthge iterates of a hyponormal operator and scalar extensions

C. Benhida, E. H. Zerouali (2009)

Studia Mathematica

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Let R and S be two operators on a Hilbert space. We discuss the link between the subscalarity of RS and SR. As an application, we show that backward Aluthge iterates of hyponormal operators and p-quasihyponormal operators are subscalar.

Exponentials of normal operators and commutativity of operators: a new approach

Mohammed Hichem Mortad (2011)

Colloquium Mathematicae

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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.

Squaring a reverse AM-GM inequality

Minghua Lin (2013)

Studia Mathematica

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Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.

Unitary dilation for polar decompositions of p-hyponormal operators

Muneo Chō, Tadasi Huruya, Kôtarô Tanahashi (2005)

Banach Center Publications

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In this paper, we introduce the angular cutting and the generalized polar symbols of a p-hyponormal operator T in the case where U of the polar decomposition T = U|T| is not unitary and study spectral properties of it.

Notes on q-deformed operators

Schôichi Ôta, Franciszek Hugon Szafraniec (2004)

Studia Mathematica

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The paper concerns operators of deformed structure like q-normal and q-hyponormal operators with the deformation parameter q being a positive number different from 1. In particular, an example of a q-hyponormal operator with empty spectrum is given, and q-hyponormality is characterized in terms of some operator inequalities.

On w-hyponormal operators

Eungil Ko (2003)

Studia Mathematica

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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.

Exponentials of bounded normal operators

Aicha Chaban, Mohammed Hichem Mortad (2013)

Colloquium Mathematicae

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The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of normal operators are given, without using the known 2πi-congruence-free hypothesis. This is a continuation of a recent work by the second author.