A separable Hilbert space is a type of Hilbert space that contains a countable dense subset. This means that within this space, any point can be approximated as closely as desired by points from this countable subset. Separable Hilbert spaces are significant because they simplify many aspects of functional analysis and quantum mechanics, making it easier to work with and understand the structure of the space.
congrats on reading the definition of Separable Hilbert Space. now let's actually learn it.