Functional calculus and representations of C0(C) on a Hilbert module
Dan Kučerovský · The Quarterly Journal of Mathematics · 2002
We prove that every representation of C0(C) on a Hilbert module satisfying certain properties in fact comes from the functional calculus for unbounded normal operators on a Hilbert module. We give a new way to construct a functional calculus for continuous (unbounded) functions of (unbounded) normal regular operators on a Hilbert module, based on an operator factorization technique. The relevant class of functions is the (unbounded) continuous functions but, in certain cases, isolated discontinuities can be allowed.