FA26

From Example Problems
Jump to: navigation, search

Let \left\{\beta _{n}\right\}\, be a sequence of real numbers such that \sum _{{n=1}}^{\infty }\alpha _{n}\beta _{n}\, is convergent for every \left\{\alpha _{n}\right\}\in l^{1}\,. Use the Uniform Boundedness theorem to prove that \left\{\beta _{n}\right\}\in l^{\infty }\,.