Alpay, D.Kaptanoǧlu, H. T.2016-02-082016-02-0820070378-620Xhttp://hdl.handle.net/11693/23477We define Toeplitz operators on all Dirichlet spaces on the unit ball of CN and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators. © Birkhäuser Verlag Basel/Switzerland 2007.EnglishArveson spaceBerezin transformBergmanBergman metricBergman projectionBesovCarleson measureDirichletHardyM - isometrySchatten - von Neumann idealToeplitz operatorUnitary equivalenceWeak convergenceWeighted shiftArticle10.1007/s00020-007-1493-11420-8989