A note on th maximal numerical range of the bimultiplication M_2,A,B

Author(s):

Abderrahim Baghdad , Mohamed Chraibi Kaadoud

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Let B(H) denote the algebra of all bounded linear opera- tors acting on a complex Hilbert space H. For A, B ∈ B(H), define the bimultiplication operator M2,A,B on the class of Hilbert-Schmidt oper- ators by M2,A,B (X) = AXB. In this paper, we show that if B∗, the adjoint operator of B, is hyponormal, then co(W0(A)W0(B)) ⊆ W0(M2,A,B ), where co stands for the convex hull and W0(.) denotes the maximal numerical range. If in addition, A is hyponormal, we show that co(W0(A)W0(B)) = W0(M2,A,B ).

Keywords:

Numerical range , maximal numerical range , normal operator , hyponormal operator , elementary operators

Language:
English
Published:
Journal of Mathematical Extension, Volume:16 Issue: 4, Apr 2022
Page:
10
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