DOI: 10.3390/sym18101732 ISSN: 2073-8994
Introduction to Spectral Property (Sbz): Symmetric Transfer Between Conjugate Operators and Drazin’s Invertible Operators
Elvis Aponte, Yasser Farhat, Vadakasi Subramanian, Ennis Rosas, Luis Mejias, Alexsander Jativa, José Soto, Jhixon MacíasIn this article, we introduce a class of operators defined through a new spectral property (Sbz), which generalizes the property (bz) studied in “Study of the property (bz) using methods from local spectral theory”. Many operators possess properties related to both their conjugate operators and their Drazin inverses; there are symmetric relationships that preserve their spectral and algebraic properties; in particular, it is shown that they share the property (Sbz). Finally, we present applications and analyze several illustrative examples.