Mon, December 16, 2019
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4:00pm [4:00pm] Sudeshna Basu: Ramakrishna Mission Vivekananda Educational and Research Institute, Belur
Description:
Analysis seminar. Speaker: Sudeshna Basu. Affiliation: Ramakrishna Mission Vivekananda Educational and Research Institute, Belur. Date and Time: Monday 16 December, 4:00 pm - 5:00 pm. Venue: Room 216, Department of Mathematics. Title: Linear Hahn Banach Extension of module homomorphisms in Hilbert and Banach modules. Abstract: The notion of linear Hahn-Banach extension operator was first studied in detail by Heinrich and Mankiewicz (1982). Previously, J. 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 via interspersing subspaces in a purely Banach space theoretic 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, Kozmider 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's space with few operators.
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