Perturbation Functions Characterizing Semi-Fredholm Multivalued Operators

The concept of measures of noncompactness for operators has been introduced and thoroughly investigated by several authors (see, for instance, [2, 4, 8]). In this work, we extend this concept to the setting of multivalued operators. We employ an axiomatic framework to define measures of noncompactness for bounded linear relations, including those associated with upper semi-Fredholm perturbations. Leveraging these measures, we derive new results for certain classes of semi-Fredholm and Fredholm multivalued operators. Lastly, we establish localization results concerning some essential spectra of bounded linear relations on Banach spaces.