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Trace class backward weighted shifts are quasisubscalar

Author(s): Eungil Ko
Journal: Proc. Amer. Math. Soc. 124 (1996), 1111-1115.
MSC (1991): Primary 47B38; Secondary 47A60
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Abstract: Recently, the author generalized Putinar techniques. In this paper we use those recent techniques and results to show (Theorem 3.1) that every trace class backward weighted shift with a monotone decreasing weight sequence is quasisubscalar.

References:

[Co]: J. B. Conway, Subnormal operators, Pitman, London, 1981. MR 83i:47030
[Ko1]: Eungil Ko, Subscalar and quasisubscalar operators, Ph.D. thesis, Indiana University, 1993.
[Ko2]: ------, Operators on a finite dimensional space, preprint.
[MP]: M. Martin and M. Putinar, Lectures on hyponormal operators, Birkhauser, Basel and Boston, 1989. MR 91c:47041
[Pu]: M. Putinar, Hyponormal operators are subscalar, J. Operator Theory, 12, (1984), 385--395. MR 85h:47027
[RR]: H. Radjavi and P. Rosenthal, Invariant subspaces, Springer-Verlag, Berlin, Heidelberg, and New York, 1973. MR 51:3924


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