Polynomially hyponormal operators
نویسندگان
چکیده
A survey of the theory of k-hyponormal operators starts with the construction of a polynomially hyponormal operator which is not subnormal. This is achieved via a natural dictionary between positive functionals on specific convex cones of polynomials and linear bounded operators acting on a Hilbert space, with a distinguished cyclic vector. The class of unilateral weighted shifts provides an optimal framework for studying k-hyponormality. Non-trivial links with the theory of Toeplitz operators on Hardy space are also exposed in detail. A good selection of intriguing open problems, with precise references to prior works and partial solutions, is offered. Mathematics Subject Classification (2000). Primary 47B20; Secondary 47B35, 47B37, 46A55, 30E05.
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