Abstract:

Let B(H) denotes the C∗-algebra of all bounded linear operators acting on the
complex Hilbert space H . In this note, we shall give some lower estimates for the injective norm
of the element
n
i=1
Ai⊗Bi in the tensor product B(H)⊗B(H), where A = (A1, ..., An) and B =
(B1, ..., Bn) are two n-tuples of elements in B(H) ; and we shall characterize the normaloid
operators in B(H) using the injective norm.
1.