Characteristic and lower characteristic of bounded linear operators

Key Points

• The aim is to introduce and define the lower characteristic of a bounded operator and its relation to operator properties.
• Introduced the lower characteristic using weak non-compactness measure.
• Proved the condition for an operator T to be upper generalized semi-Fredholm based on its lower characteristic.
• Established that if the lower characteristic of T is strictly positive, then T is upper generalized semi-Fredholm.
• Provided an application of these concepts to Markov chains.