On the Generalized Functional Calculus for Non-Normal Operators
Wai-Fong Chuan · Journal of the London Mathematical Society · 1986
We prove that for each bounded linear operator T on a Hilbert space, the set of all continuous decomposable functions on Ti form a C∗-algebra ∗-isomorphic with the unital C∗-algebra generated by T. These results generalize the spectral theorem for normal operators. Necessary and sufficient conditions for singly generated unital C∗-algebras to be ∗-isomorphic are also obtained.