Media Summary: Weak compactness and weak sequential compactness. Uniformly convex spaces. Examples and other equivalent ... Definition and examples of separable metric spaces and Banach spaces. Separability of the dual implies separability of the space. Review of normed spaces and linear bounded operators. The dual of a normed space. Examples of dual spaces.
Math400 Functional Analysis Section 4 - Detailed Analysis & Overview
Weak compactness and weak sequential compactness. Uniformly convex spaces. Examples and other equivalent ... Definition and examples of separable metric spaces and Banach spaces. Separability of the dual implies separability of the space. Review of normed spaces and linear bounded operators. The dual of a normed space. Examples of dual spaces. Convex sets and linear operators in the weak topology. The weak topology as a vector space topology. Definition and basic properties of the weak star topology of the dual of a normed space. Definition and some basic properties of the weak topology and weak convergence.
Other characterizations of reflexivity. Illustration of the use of reflexivity in the calculus of variations. Definition and examples of topological spaces. The subspace topology. Comparison of topologies. Bases Exercises on total boundedness and equicontinuity.
