Separately radial and radial Toeplitz operators on the projective space and representation theory |
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Authors: | Raul Quiroga-Barranco Armando Sanchez-Nungaray |
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Institution: | 1.Centro de Investigación en Matemáticas,Guanajuato,Mexico;2.Facultad de Matemáticas,Universidad Veracruzana,Xalapa Enríquez,Mexico |
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Abstract: | We consider separately radial (with corresponding group T n ) and radial (with corresponding group U(n)) symbols on the projective space P n (C), as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the C*-algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the commutativity of the C*-algebras is a consequence of the existence of multiplicity-free representations. Furthermore, our method shows how to extend the current formulas for the spectra of the corresponding Toeplitz operators to any closed group lying between T n and U(n). |
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