ABSTRACT

In chapter 9, we prove Steinhaus theorem that a matrix cannot be both a regular and a Schur matrix. We then introduce the concept of a Steinhaus type theorem and prove several Steinhaus type theorems in the remaining part of the chapter. We also give instances where functional analytic tools like the Unuform Boundedness Principle are used to prove important results in Summability. With chapter 9,we conclude the Summability component of the book.