Norm Inequalities Related To P-Schatten Class Operator

Functional analysis is an important branch of modern mathematics.Operator alge-bra is one of the core contents of functional analysis.Because operator algebra plays an important role in mathematics and other disciplines,it has been greatly developed in the first 30 years of the 20th century.Norm inequality is an important part of the research of operator algebra.Many mathematicians have obtained some famous norm inequalities through the studying of operators.Moreover,they got refinements and applications of related inequalities.Clarkson inequality is one of them and it plays an important role in functional analysis so that many scholars are studying it.It plays a vital role in analytics,operator theory,mathematical physics and so on.In this paper,we study and extend some norm inequalities of p-Schatten operators,and we obtain some related norm inequalities.We also study Clarkson inequalities for n-tuples which are not commutative,and we obtain some refinements about commutative Clarkson inequalities for n-tuples of vectors.The thesis consists of four chapters and is organized as follows.Chapter 1 introduce the research background of the thesis,the related concepts and some existing results.Chapter 2 extend some norm inequalities of p-Schatten operators and obtain some norm inequalities of p-Schatten operators.Chapter 3 introduce some refinements about commutative Clarkson inequalities for n-tuples of vectors.The summary of this paper is proposed in Chapter 4,we put forward the unresolved issues and the direction of efforts.