Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space
2013 ◽
Vol 2013
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pp. 1-12
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Keyword(s):
We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols.
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2012 ◽
Vol 2012
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pp. 1-16
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Keyword(s):
2009 ◽
Vol 2009
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pp. 1-16
2009 ◽
Vol 86
(1)
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pp. 45-60
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