A maximally monotone operator is a specific type of monotone operator that cannot be extended any further without losing its monotonicity property. This means that if you have a monotone operator, it is maximally monotone if there are no other monotone operators that contain it as a proper subset. This concept is crucial in understanding the relationships between different operators and their properties in variational analysis.
congrats on reading the definition of maximally monotone operator. now let's actually learn it.