On Similarity And Reducing Subspaces Of Multiplication Operator On The Weighted Bergman Space Of The Bidisk

In this paper,we invetigate the similarity and reducing subspaces of multiplication operator on the weighted Bergman space of the bidisk.Let be the weighted Bergman space of the bidisk in C2.We prove that the multiplieation operator is similar to Besides that,using the matrix manipulations combined with operator theory methods,we characterize the reducing subspaces of on,First we get and are both the minimal reducing subspaces for.In fact,every reducing subspace for is a direct sum of some minimal reducing subspaces which described as and So the number of the reducing subspaces for is exactly infinite.Then,by defining the full reducing subspace,we also get the reducing subspaces for which consist of the direct sum of full reducing subspaces are where,And the number of the reducing subspaces for which consist of the direct sum of full reducing subspaces is...