Hyponormal dual Toeplitz operators on the orthogonal complement of the Fock space
Fock space is an important analytic function space composed of entire functions.Because it is related to the representation theory of Heisenberg group in quantum mechanics,Fock space has important research significance not only in the operator theory of function space,but also closely re-lated to the study of quantum mechanics.Dual Toeplitz operator is also one of the research contents in operator theory,interacting with Toeplitz operator.The hyponormality of operators,which origi-nated from the fifth problem in Halmon's book named"A Hilbert Space Problem",has always been one of the key research contents in operator theory.In this paper,we use the structure of function space and the properties of dual Toeplitz operators to characterize the hyponormality of dual Toeplitz operator with symbol(z-a)(z-b)on the orthogonal complement of Fock space,and obtain that its hyponormality is equivalent to normality.We also explore some necessary conditions for the dual Toeplitz operator with the harmonic polynomial symbol to be hyponormal.
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