Add to ORKGAbstract. Let (H) denote the algebra of operators on a Hilbert space H into itself. Let d = δ or, where δAB:(H)→(H) is the generalized derivation δAB(S)=AS−SB and AB: (H) → (H) is the elementary operator AB(S) = ASB−S. Given A,B,S ∈ (H), we say that the pair (A,B) has the property PF(d(S)) if dAB(S) = 0 implies dA∗B∗(S) = 0. This paper characterizes operators A,B, and S for which the pair (A,B) has property PF(d(S)), and establishes a relationship between the PF(d(S))-property of the pair (A,B) and the range-kernel orthogonality of the operator dAB. 2000 Mathematics Subject Classification. 47A62, 47B47, 47B10
Let L(H) denote the algebra of bounded linear operators on a complex separable and infinite dimensio...
AbstractLet H be a separable infinite dimensional complex Hilbert space and let B(H) denote the alge...
Let A be a Banach algebra and ℒ(A) the algebra of all bounded linear operators acting on A. For a; b...
Abstract. Let (H) denote the algebra of operators on a Hilbert space H into itself. Let d = δ or, wh...
Let ℬ(H) denote the algebra of operators on a Hilbert space H into itself. Let d=δ or Δ, where δAB:ℬ...
AbstractLet H be a separable infinite dimensional complex Hilbert space, and let B(H) denote the alg...
summary:Let $L(H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $...
summary:Let $L(H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $...
summary:Let $L(H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $...
Copyright c © 2014 A. Bachir. This is an open access article distributed under the Creative Commons ...
Abstract. The familiar Fuglede-Putnam Theorem is as follows (see [5], [11] and [12]): If A and B are...
We prove the orthogonality (in the sense of Birkhoff) of the range and the kernel of an important cl...
We are interested in the investigation of the orthogonality (in the sense of Birkhoff) of the range ...
Abstract. The equation AX = XB implies A∗X = XB ∗ when A and B are nor-mal operators is known as the...
Let H be a separable infinite dimensional complex Hilbert space, and let B(H) denote the algebra of ...
Let L(H) denote the algebra of bounded linear operators on a complex separable and infinite dimensio...
AbstractLet H be a separable infinite dimensional complex Hilbert space and let B(H) denote the alge...
Let A be a Banach algebra and ℒ(A) the algebra of all bounded linear operators acting on A. For a; b...
Abstract. Let (H) denote the algebra of operators on a Hilbert space H into itself. Let d = δ or, wh...
Let ℬ(H) denote the algebra of operators on a Hilbert space H into itself. Let d=δ or Δ, where δAB:ℬ...
AbstractLet H be a separable infinite dimensional complex Hilbert space, and let B(H) denote the alg...
summary:Let $L(H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $...
summary:Let $L(H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $...
summary:Let $L(H)$ denote the algebra of operators on a complex infinite dimensional Hilbert space $...
Copyright c © 2014 A. Bachir. This is an open access article distributed under the Creative Commons ...
Abstract. The familiar Fuglede-Putnam Theorem is as follows (see [5], [11] and [12]): If A and B are...
We prove the orthogonality (in the sense of Birkhoff) of the range and the kernel of an important cl...
We are interested in the investigation of the orthogonality (in the sense of Birkhoff) of the range ...
Abstract. The equation AX = XB implies A∗X = XB ∗ when A and B are nor-mal operators is known as the...
Let H be a separable infinite dimensional complex Hilbert space, and let B(H) denote the algebra of ...
Let L(H) denote the algebra of bounded linear operators on a complex separable and infinite dimensio...
AbstractLet H be a separable infinite dimensional complex Hilbert space and let B(H) denote the alge...
Let A be a Banach algebra and ℒ(A) the algebra of all bounded linear operators acting on A. For a; b...