Weighted n-shifts and M-hyponormality (Q1067578)

Weighted shifts are generalized by defining weighted n-shifts on a separable complex Hilbert space. The two main results of the paper provide a technique to produce a lot of examples of M-hyponormal weighted n-shifts with operator weights and with scalar weights. The only non- hyponormal M-hyponormal operator that was known previously was given by \textit{B. L. Wadhwa} [Duke Math. J. 41, 655-660 (1974; Zbl 0292.47021)] viz: weighted shift with weights 1,2,1,1,1... Also, hyponormal, quasi- hyponormal, paranormal weighted n-shifts and weighted n-shifts of class(M) are characterized. Examples are provided to show that the inclusion relations \[ (1)\quad hyponormal\quad \subseteq \quad M- hyponormal\quad \cap \quad quasi-hyponormal\quad \cap \quad class(M) \] and \[ (2)\quad class(N,k)\quad \cap \quad M-hyponormal\quad \subseteq \quad normaloid\quad \cap \quad M-hyponormal \] are proper.