Algebraic Variant of Noether Operator Theory

Key Points

• The aim is to establish a framework for Noether operators in normless linear spaces and examine their properties.
• Constructed the theory of Noether operators in linear spaces without norm and topology.
• Investigated the correspondence among elements defined by Noether operators.
• Identified necessary and sufficient conditions for the Noetherness of linear operators.
• Determined specific properties of characteristic Noether operators.
• Developed methods for the regularization of these operators.
• Provided significant conditions that validate the existence of Noether operators.