Applied Mathematics Colloquium: Dr. Sudeshna Basu

TITLE : LINEAR HAHN-BANACH TYPE EXTENSION OPERATORS IN BANACH ALGEBRAS OF OPERATORS

Abstract ; The notion of linear Hahn-Banach extension operator was first studied in detail by Heinrich and Mankiewicz(1982) . Previously, Lindenstrauss (1966) studied similar versions of this notion in the context of non-separable reflexive Banach spaces. Subsequently, Sims and Yost (1989)  proved the existence of linear Hahn-Banach extension operators in a purely Banach space theoretical set up. In this paper, we study similar questions in the context of Banach modules and module homomorphisms, in particular, Banach algebras of operators on Banach spaces. Based on Dales, Kania, Kochanek, Koszmider and Laustsen (2013), and also Kania and Laustsen(2017) , we give complete answers for reflexive Banach spaces and the non-reflexive space constructed by Kania and Laustsen from the celebrated Argyros-Haydon space with very few operators.