On reflexivity of closed unital subalgebras in locally convex spaces (Q2725241)

Let \(B\) be an equicontinuous Boolean algebra of projections in a barrelled locally convex Hausdorff space \(X\), \(M= \overline{\text{span}(B)}\), where the closure is taken in the weak operator topology and \(\text{AlgLat }B\) the algebra of all operators on \(X\) which leave left invariant all \(B\)-invariant closed subspaces of \(X\). The main result of this work states that for \(T\in L(X)\) we have NEWLINE\[NEWLINET\in M\text{ if and only if }T\in \text{AlgLat }B.NEWLINE\]NEWLINE As a consequence it is shown that each unital closed subalgebra of \(M\) is reflexive.