On the spectrum of Toeplitz operators with quasi-homogeneous symbols

Abstract

In this paper, we fully describe the spectrum of a Toeplitz operator with quasi-homogeneous symbol and give formulas for the calculation of the spectral radius in the case where it is maximal. Finally, Theorem 4 gives equivalent conditions on the quasi-homogeneous function F to have ‖TF‖ = ‖F‖∞ . As a corollary we obtain some necessary and sufficient conditions for such Toeplitz operators to verify the equality σ(TF) = F( ) . Mathematics subject classification (2010): 47B35.