Which 2-hyponormal 2-variable weighted shifts are subnormal? Original Research Article

It is well known that a 2-hyponormal unilateral weighted shift with two equal weights must be flat, and therefore subnormal. By contrast, a 2-hyponormal 2-variable weighted shift which is both horizontally flat and vertically flat need not be subnormal. In this paper we identify a large class image of flat 2-variable weighted shifts for which 2-hyponormality is equivalent to subnormality. One measure of the size of image is given by the fact that within image there are hyponormal shifts which are not subnormal.