Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols

Abstract EN

We construct an operator R whose restriction onto weighted pluriharmonic Bergman Space bμ2(Bn) is an isometric isomorphism between bμ2(Bn) and l2#.

Furthermore, using the operator R we prove that each Toeplitz operator Ta with radial symbols is unitary to the multication operator γa,μI.

Meanwhile, the Wick function of a Toeplitz operator with radial symbol gives complete information about the operator, providing its spectral decomposition.