Hilbert Spaces

1 Hilbert Spaces

Recall that an Inner Product Space is a vector space with an inner product, which induces a norm and hence a metric (see Normed Space).

A Hilbert space is a complete inner product space, meaning that every Cauchy Sequence in the space converges to a limit within the space.

Standard examples are \(\mathbb{R}^n\) with the dot product, the sequence space \(\ell^2\), and \(L^2(\mu)\) for a measure space \((X,\mathcal{M},\mu)\).

Backlinks

• Analysis
• Conditional Expectation
• Functional Analysis
• Inner Product Space
• Itô Process
• Krasnoselskii-Mann Iteration
• Normed Space
• Orthogonality and Projections
• Stochastic Differential Equations