ON THE RANGE OF THE ELEMENTARY OPERATOR X ↦ AXA − X

2008 ◽  
Vol 108 (1) ◽  
pp. 1-6
Author(s):  
Said Bouali ◽  
Youssef Bouhafsi
Keyword(s):  
Elementary Operator

Additive maps having a generalized derivation expansion

2015 ◽  
Vol 14 (04) ◽  
pp. 1550048 ◽  
Author(s):  
Tsiu-Kwen Lee
Keyword(s):  
Central Simple Algebra ◽  
Simple Algebra ◽  
Generalized Derivation ◽  
Elementary Operator ◽  
Additive Map ◽  
Finite Dimensional ◽  
Left And Right ◽  
Central Simple ◽  
Skolem Theorem ◽  
Additive Maps

Let R be a prime ring with extended centroid C. We prove that an additive map from R into RC + C can be characterized in terms of left and right b-generalized derivations if it has a generalized derivation expansion. As a consequence, a generalization of the Noether–Skolem theorem is proved among other things: A linear map from a finite-dimensional central simple algebra into itself is an elementary operator if it has a generalized derivation expansion.

On the invertibility of length two elementary operators

2015 ◽  
Vol 30 ◽  
pp. 916-913
Author(s):  
Janko Bracic ◽  
Nadia Boudi
Keyword(s):  
Banach Space ◽  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Elementary Operator ◽  
Bounded Linear Operators ◽  
Existence Of A Solution ◽  
Bounded Linear ◽  
Elementary Operators ◽  
Necessary And Sufficient

Let X be a complex Banach space and L(X) be the algebra of all bounded linear operators on X. For a given elementary operator P of length 2 on L(X), we determine necessary and sufficient conditions for the existence of a solution of the equation YP=0 in the algebra of all elementary operators on L(X). Our approach allows us to characterize some invertible elementary operators of length 2 whose inverses are elementary operators.

scholarly journals Some versions of Anderson's and Maher's inequalities II

2003 ◽  
Vol 2003 (53) ◽  
pp. 3355-3372
Author(s):  
Salah Mecheri
Keyword(s):  
Elementary Operator

We are interested in the investigation of the orthogonality (in the sense of Birkhoff) of the range of an elementary operator and its kernel.

scholarly journals A generalized commutativity theorem for pk-quasihyponormal operators

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 77-83
Author(s):  
B.P. Duggal
Keyword(s):  
Hilbert Space ◽  
Generalized Derivation ◽  
Elementary Operator ◽  
Commutativity Theorem ◽  
Hilbert Space Operators

For Hilbert space operators A and B, let ?AB denote the generalized derivation ?AB(X) = AX - XB and let /\AB denote the elementary operator rAB(X) = AXB-X. If A is a pk-quasihyponormal operator, A ? pk - QH, and B*is an either p-hyponormal or injective dominant or injective pk - QH operator (resp., B*is an either p-hyponormal or dominant or pk - QH operator), then ?AB(X) = 0 =? SA*B*(X) = 0 (resp., rAB(X) = 0 =? rA*B*(X) = 0). .

scholarly journals Norm equality for a basic elementary operator

2003 ◽  
Vol 286 (1) ◽  
pp. 359-362 ◽  
Author(s):  
Mohamed Barraa ◽  
Mohamed Boumazgour
Keyword(s):  
Elementary Operator ◽  
Norm Equality

scholarly journals On the Putnam-Fuglede theorem

2004 ◽  
Vol 2004 (53) ◽  
pp. 2821-2834
Author(s):  
Yin Chen
Keyword(s):  
Elementary Operator ◽  
Asymptotic Results ◽  
Second Degree

We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpotents. Some asymptotic results are also given.

scholarly journals Putnam-Fuglede theorem and the range-kernel orthogonality of derivations

2001 ◽  
Vol 27 (9) ◽  
pp. 573-582 ◽  
Author(s):  
B. P. Duggal
Keyword(s):  
Hilbert Space ◽  
Generalized Derivation ◽  
Elementary Operator ◽  
Algebra Of Operators

Letℬ(H)denote the algebra of operators on a Hilbert spaceHinto itself. Letd=δorΔ, whereδAB:ℬ(H)→ℬ(H)is the generalized derivationδAB(S)=AS−SBandΔAB:ℬ(H)→ℬ(H)is the elementary operatorΔAB(S)=ASB−S. GivenA,B,S∈ℬ(H), we say that the pair(A,B)has the propertyPF(d(S))ifdAB(S)=0impliesdA∗B∗(S)=0. This paper characterizes operatorsA,B, andSfor which the pair(A,B)has propertyPF(d(S)), and establishes a relationship between thePF(d(S))-property of the pair(A,B)and the range-kernel orthogonality of the operatordAB.

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