Lambert conditional operators on $C^*$-algebras

چکیده مقاله

In this paper, for each a ∈ A we introduce an algebra Ka ⊆ K of bounded Lambert
conditional operators on a unital C∗-algebra A, which is defined in terms of the left
multiplication operators and conditional expectations. The commutant ofK is studied,
as well as the question of when K is closed in the norm operator topology.