On Similarity And Reducing Subspaces Of Analytic Toeplitz Operator On The Weighted Sobolev Disk Algebra

Toeplitz operator is a class of important operators in operator theory and operator algebra.On the Hardy space and the Bergman space,a series of properties of analytic Toeplitz operator have been researched by many scholars.These properties include compactness,similarity,reducing subspaces and so on.In this paper,we mainly discuss similarity and reducing subspaces of analytic Toeplitz operators with symbol zn on the weighted Sobolev disk algebra.The main results and innovation points are as follows:1.It is showed that ek（z）=（?）（k=0,1,…）forms an orthonormal basis of the weighted Sobolev disk algebra SA（D,dAα）;2.It is proved that for i,j,0≤i≠j