In this paper we continue our study, begun in , of the relationships between an arbitrary operator T on Hubert space and its Aluthge transform T̃. In particular, we show that in most cases the spectral picture of T coincides with that of T̃, and we obtain some interesting connections between T and T̃ as a consequence.
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Acknowledgement. This paper was written while the third author was visiting Korea in 1999. The first author was supported by KOSEF 971-0102-006-2. The second author was supported by the MOST through National R&D program (97-N6-01-01-A-5) for Women's Universities. The third author acknowledges support from the National Science Foundation.