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.
DOI: http://dx.doi.org/10.7900/jot.2012may24.1969
Keywords: Toeplitz operators, paragrassmann algebras, quantum
spaces, reproducing kernels
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