The spectral theorem for normal operators on a Clifford module

In this paper, using the recently discovered notion of S-spectrum, we prove spectral theorem for a bounded or unbounded normal operator on Clifford module (i.e., two-sided Hilbert over algebra based units that all square to be $$-1$$ ). Moreover, establish existence Borel functional calculus operators module. Towards end, have developed many results analysis, theory, integration theory and measure in setting which may an independent interest. Our is natural Dirac manifolds non-self adjoint case. our provide new class n-tuples commuting non-commuting real complex space. special space complementary J. L. Taylor.