On the range-kernel orthogonality of elementary operators

Title:

On the range-kernel orthogonality of elementary operators

Creator:

Bouali, Said and Bouhafsi, Youssef

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:92510018-69b8-4cd5-917b-56b7af29a27e
uuid:92510018-69b8-4cd5-917b-56b7af29a27e
doi:10.21136/MB.2015.144393

Subject:

derivation, elementary operator, orthogonality, unitarily invariant norm, cyclic subnormal operator, and Fuglede-Putnam property

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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)=AX-XB and δ A,B}(X)=AXB-X for all X\in 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 L(H).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

261-269

Source:

Mathematica bohemica | 2015 Volume:140 | Number:3

Harvested from:

CDK

Metadata only:

false