This chapter deals mainly with the geometry of (primarily abstract) Hilbert spaces. In Chapter 5, Hilbert space theory is combined with distribution theory to establish the theory of L 2 spaces, on which much of modern functional analysis is based.
KeywordsConnection with finite-dimensional spaces Hilbert space axioms the Schwarz and triangle inequalities Connection with finite-dimensional spaces Hilbert space axioms the Schwarz and triangle inequalities the parallelogram law and the connection with general Banach spaces completeness of I2 transfinite cardinal numbers equivalence of separable Hilbert spaces Hilbert spaces of larger dimensions separability of Fock spaces completeness criteria for orthonormal sequences linear functionals the Riesz-Fischer and Riesz-Fréchet theorems strong and weak convergence polarization of quadratic functionals
Unable to display preview. Download preview PDF.