Friday, May 25, 2012

1205.5493 (Stephen Bruce Sontz)

Paragrassmann Algebras as Quantum Spaces, Part II: Toeplitz Operators    [PDF]

Stephen Bruce Sontz
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.
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