Unitary Equivalence Of High-dimensional Space Of Toeplitz Operators On Function Spaces Of Analytic Functions Best Approximation Of Functions And Extremum

This paper is addressed to discuss two problems: the one is about the unitaryequivalence of Toeplitz operators on Bergman spaces and Dirichlet spaces whichis more complex than that on the classic Hardy spaces. The other is to extend theresult deriving from Hahn-Banach theory about the best approximation and the dualextremal function of analytic functions in the 1-dim spaces to the n-dim spaces.