Extending Uniform Boundedness Principle

In this paper we mainly discuss the late extending styles of basic principles such as equicontinuity principle ,uniform boundedness principle ,Banach-Steinhaus theorem and ect., and describe the new characters of these new results in Banach space. Consisting of 3 Chapters, the Paper mainly includes the following contents: Chapter 1 of Introduct on presents the significance of extending uniform boundedness principle and elso reviews one hundred years' development of uniform boundedness principle iind the work done by people in this aspect; Chapter 2 mainly introduce some preparatory knowledge including definitions of dissecting operators, absorbing operators, equicontinuity and some relative examples; In Chapter 3, We discuss the new researching results of equicontinuity principle,uniform boundedness principle and Banach-Steinhaus type theorem .We also give the showing style of these principles in Banach space and give some applied examples of them.