Abstract. We discuss the relationship between the n-reflexivity of a linear sub-space S in B(Ji), property (A.\/ n ), Class Co and strictly /^-separating vectors. We also show that every algebraic operator with property (A2) is hyperreflexive. (Tx, Sx): x e Ji, \\x\\ < 1}. The smallest such K = K(S) is the constant of hyperreflexivity of 0 such that \\S\M\\ > e\\S\\, for all S eS. It is easily seen that M is a strictly separating subspace for S if and only if the only member S € S satisfying S(M) = (0} is S = 0 and S \ M is norm closed.For vectors x and y in Ti, we write x®y for the rank one operator defined by (x y)(u) = (u, y)x, u 6 H. Let S C B(H) be a weak*-closed subspace and n is a positive integer. We say that S has property (Ai/,,) if every weak*-continuous functional
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