Inequalities Related To P-schatten Class And Its Applications

From the 19th century to the 20th century, the analysis mathematics trended to ab-straction. Searching for the universality and unity of the conclusions and methods is its outstanding feature. And functional analysis is produced in the process. Functional anal-ysis is the important branch of the modern mathematics. Operator algebra, is the core content of Functional analysis. Norm inequalities is an important part of the study of operator algebra. By studying operators in inner product space, many mathematicians ob-tained some celebrated norm inequalities. Moreover, they got refinements and applications related to these norm inequalities. In this paper, under the foundation of inner product,we study some inequalities and their applications. The main contents are as follows:The first part is introduction. We mainly introduce Hilbert space, besides, we also introduce some theorems and knowledge that are referred frequently in this paperThe second part, we give some norm inequalities related to p-Schatten class.The third part, we give some non-commutative Clarkson inequalities for n-tuples of operators.The forth part, we give Schatten p-norm inequalities of k sets of operators related to an extended operator parallelogram law.