The Lebesgue-Stieltjes Integral. (B)-Measurable Sets and Operators in Metric Spaces. Groups. General Vector Spaces. F-Spaces. Normed Spaces. Banach Spaces. Compact Operators. Biorthogonal Sequences. Linear Functionals. Weakly Convergent Sequences. Linear Functional Equations. Isometry, Equivalence, Isomorphism. Linear Dimension. Appendix: Weak Convergence in Banach Spaces.
Some Aspects of the Present Theory of Banach Spaces by A. Pelczyński and Cz. Bessaga. Reflexive and Weakly Compactly Generated Banach Spaces. Related Counter Examples. Local Properties of Banach Spaces. The Approximation Property and Bases. Characterizations of Hilbert Spaces in the Class of Banach Spaces. Classical Banach Spaces. The Topological Structure of Linear Metric Spaces.