Quaternionic Non-Selfadjoint Operators and Their Spectral Theory

Explore the complexities of spectral theory for quaternionic and Clifford-algebra-valued operators in this 39-minute conference talk by Uwe Kähler from the University of Aveiro. Delve into the challenges posed by noncommutativity in classic spectral theory methods and examine the differences between left and right spectra in finite rank operators. Learn about the S-spectrum as a natural approach to noncommutative settings and its application to quaternionic non-selfadjoint operators. Investigate quaternionic Volterra operators and triangular representations of quaternionic operators, drawing parallels to classic approaches. Discover spectral integral representations with respect to quaternionic chains and explore the concept of P-triangular operators in the quaternionic context. Gain insights into the localization of spectra for non-selfadjoint quaternionic operators in this advanced mathematical presentation.