Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 396
Left and right multiplication operators and (m, n)-isosymmetries
Hamza Lakrimi, Mohamed Amouch
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2335
April 15, 2335

Abstract: Let H be a complex Hilbert space, B(H) the algebra of all bounded linear operators on H and ( C2 (H), ||.||_2 ) the ideal of Hilbert-Schmidt operators. For A, B ϵ B (H), let L_A ϵ B(B(H)), and R_B ϵ B(B(H)) be the left and the right multiplication operators, respectively. The two-sided multiplication M_A,B ϵ B(B(H)) is defined by M_A,B (X)=(L_A-R_B)(X)=AXB and the generalized derivation ẟ_A,B ϵ B(B(H)) is defined by ẟA,B =( L_A - R_B)(X)=AX-XB. The aim objective of this presentation is to study the transmission of property of being (m, n)-isosymmetry from operators A ...