(International Journal of Mathematical Analysis, 2019) Odero, Beatrice Adhiambo; Agure, J. O.; Nyamwala, F. O.
Let H be an infinite dimensional complex Hilbert space and A, B ∈ B(H)
where B(H) is the C
∗
-algebra of all bounded linear operators on H. Let
MAB : B(H) → B(H) be a multiplication operator induced by A and B defined by
MAB(X) = In this paper we show that the numerical range of multiplication operator
is given by
V (MAB/B(B(H))) = [S
U∈U(H) W(U
∗AUB)
−]
− for all A, B ∈ B(H)
and U a unitary operator on the algebra B(H) where V is the algebraic numerical range and W is the classical numerical range. The results obtained
are an extension of the the work done by Barraa [4].
Mathematics Subject Classification: Primary 47A12, Secondary 47A30,
47B47
