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Journal of Operator Theory

Volume 71, Issue 2,  Spring  2014  pp. 411-426.

Paragrassmann algebras as quantum spaces, Part II: Toeplitz Operators

Authors:  Stephen Bruce Sontz
Author institution: Centro de Investigacion en Matematicas, A.C., (CIMAT), Guanajuato, 36240, Mexico

Summary:  This paper continues the study of paragrassmann algebras begun in part I with the definition and analysis of Toeplitz operators in the associated holomorphic Segal--Bargmann space. These are defined in the usual way as multiplication by a symbol followed by the projection defined by the reproducing kernel. These are non-trivial examples of spaces with Toeplitz operators whose symbols are not functions and which themselves are not spaces of functions.

Keywords:  Toeplitz operators, paragrassmann algebras, quantum spaces, reproducing kernels

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