Geodesic
The evaluation functionals associated with an algebra of bounded operators
Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 73-76

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In this note we shall employ the notation of [1] without further mention. Thus X denotes a normed space and P the subset of X × X′ given byGiven a subalgebra of B(X), the set {Φ(X,f):(x,f) ∈ P} of evaluation functional on is denoted by II. We shall prove that if X is a Banach space and if contains all the bounded operators of finite rank, then Π is norm closed in ′. We give an example to show that Π need not be weak* closed in ′′. We show also that FT need not be norm closed in ′′ if X is not complete. 
Duncan, J. The evaluation functionals associated with an algebra of bounded operators. Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 73-76. doi: 10.1017/S0017089500000574
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[1] 1.Bonsall, F. F., The numerical range of an element of a normed algebra, Glasgow Math. J. 10 (1969), 68–72. Google Scholar | DOI

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