Chapter V

Hilbertian spaces¹ (elementary theory)

Throughout this chapter, K denotes the field R or the field C. For every complex number $\xi = \alpha + i\beta$ ($\alpha, \beta$ real), $\bar{\xi}$ denotes the conjugate $\alpha - i\beta$ of $\xi$; in particular, we have $\bar{\xi} = \xi$ if and only if $\xi$ is real.