A Hilbert scale is a family of Hilbert spaces Hs,s∈RHs,s∈R such that
for every s,t∈Rs,t∈R with s < t, Ht⊆HsHt⊆Hs and the inclusion
operator is continuous. Given a Hibert space, we show how to construct
a Hilbert scale with H0=HH0=H using the concept of Gelfand
triple and give examples of Hilbert scales which are generated by
compact operators between Hilbert spaces as well as closed densely
defined unbounded operators. Citing results from some of the recent
work of the author, we discuss the use of Hilbert scales while deriving
error estimates for ill-posed operator equations.
