Density of the polynomials in Hardy and Bergman spaces of slit domains

It is shown that for any t, 0 <t<infinity, there is a Jordan are Gamma with endpoints 0 and 1 such that Gamma\{1}subset of D:={z:vertical bar z vertical bar <1} and with the property that the analytic polynomials are dense in the Bergman space A(t) (D\Gamma). It is also shown that one can go further in the Hardy space setting and find such a Gamma that is in fact the graph of a continuous real-valued function on [0,1], where the polynomials are dense in H(t) (D\Gamma); improving upon a result in an earlier paper.