Multiple Similarity Equivalence Between The Submodule On The Bidisc Hardy Space

In this paper we mainly study the equivalence relation between the submodules on the bidisc Hardy space.On the basis of unitary equivalence,we study further mul-tiple similarity equivalence relation on the submodules and discuss some problems of operator spectrum.In the first chapter, we discuss some relevant research background and give some basic concepts and main results.In the second chapter, we introduce some knowledge, some basic concepts and notations.In the third chapter, we discuss the necessary and sufficient conditions of re-similarity equivalence between the two submodules.In the fourth chapter, we discuss the relevant knowledge of operator spectrum.