Abstract

We study some algebraic properties of Toeplitz operators  with radial and quasi homogeneous symbols on the pluriharmonic Fock space over $\mathbb{C}^{n}$. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator, the zero-product problem for the product of two Toeplitz operators.  Next we characterize the commutativity of Toeplitz operators with quasi homogeneous symbols and finally we study finite rank of the product of Toeplitz operators with quasi homogeneous symbols.

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