TY - JOUR
T1 - A note concerning the numerical range of a basic elementary operator
AU - Boumazgour, Mohamed
AU - Nabwey, Hossam A.
N1 - Publisher Copyright:
© 2016 by the Tusi Mathematical Research Group.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H, and let S be a norm ideal in B(H). For A, B ∈ B(H), define the elementary operator M S, A, B on S by M S, A, B(X) = AXB (X ∈ S). The aim of this paper is to give necessary and suffcient conditions under which the equality V (M S, A, B) = cō(W(A)W(B)) holds. Here V (T) and W(T) denote the algebraic numerical range and spatial numerical range of an operator T, respectively, and cō(Ω) denotes the closed convex hull of a subset Ω⊆ C.
AB - Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H, and let S be a norm ideal in B(H). For A, B ∈ B(H), define the elementary operator M S, A, B on S by M S, A, B(X) = AXB (X ∈ S). The aim of this paper is to give necessary and suffcient conditions under which the equality V (M S, A, B) = cō(W(A)W(B)) holds. Here V (T) and W(T) denote the algebraic numerical range and spatial numerical range of an operator T, respectively, and cō(Ω) denotes the closed convex hull of a subset Ω⊆ C.
KW - Elementary operators
KW - Norm ideals
KW - Numerical range
KW - Spectrum
UR - https://www.scopus.com/pages/publications/85046494784
U2 - 10.1215/20088752-3605510
DO - 10.1215/20088752-3605510
M3 - Article
AN - SCOPUS:85046494784
SN - 2008-8752
VL - 7
SP - 434
EP - 441
JO - Annals of Functional Analysis
JF - Annals of Functional Analysis
IS - 3
ER -