ABSTRACT

In this chapter we consider two important locally convex topologies: the weak topology on a normed space X $ \mathcal{X} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315151601/40b40f18-f94e-4633-83f0-b519efc5b015/content/inline-math10_1.tif"/> and the weak ∗ $ ^* $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315151601/40b40f18-f94e-4633-83f0-b519efc5b015/content/inline-math10_2.tif"/>  topology on its dual X ′ $ \mathcal{X}^{\prime } $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315151601/40b40f18-f94e-4633-83f0-b519efc5b015/content/inline-math10_3.tif"/> . The chapter relies on some of the material developed in Sections 9.1–9.3.