Joint Spectral Theory Using Clifford Algebra

Spectral theory is the study of eigenvalues and eigenvectors of operators or matrices on Hilbert spaces. If we study more than one operator, then the spectrum is generalized to the joint spectrum. Various spectra have been defined by different authors for a collection of operators. Pryde and McIntosh introduced a new operator named Clifford operator and a spectral set associated with a collection of operators to study its joint spectra. We further explored the joint spectrum and proved interesting perturbation results and inequalities using the Clifford operator.