We say that an operator T on a Hilbert space H has the Bishop's property (β) if for an arbitrary open set U ⊂ C and analytic functions f n : U → H with ∥(T − z) f n (z)∥ converges to 0 uniformly on every compact subset of U as n → ∞ then ∥ f n ∥ converges to 0 uniformly on every compact subset of U as n → ∞. An operator T on H is called to be hyponormal if T * T ≥ TT *, and T is called to be class A if T * T ≤ |T 2 |. In this papaer, we give an elementary proof of the assertion that every hyponormal operator has the Bishop's property (β). And we show that every class A operator has the Bishop's property (β). Moreover, we also show a class A operator T is similar to a hyponormal operator if T is invertible, and hence T has the growth condition (G 1).