Linear Hahn-Banach type extension operators in Banach algebras of operators
Copyright policy )Linear Hahn-Banach type extension operators in Banach algebras of operators
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.
Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), 46A22, 46B20, 46B28, 46H10, 47L10, Theorems of Hahn-Banach type; extension and lifting of functionals and operators, Hahn-Banach extension property, Functional Analysis (math.FA), Mathematics - Functional Analysis, left-module homomorphism, Algebras of operators on Banach spaces and other topological linear spaces, Ideals and subalgebras, FOS: Mathematics, algebra of operators acting on a Banach space, Argyros-Haydon space, Spaces of operators; tensor products; approximation properties, Banach module
Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), 46A22, 46B20, 46B28, 46H10, 47L10, Theorems of Hahn-Banach type; extension and lifting of functionals and operators, Hahn-Banach extension property, Functional Analysis (math.FA), Mathematics - Functional Analysis, left-module homomorphism, Algebras of operators on Banach spaces and other topological linear spaces, Ideals and subalgebras, FOS: Mathematics, algebra of operators acting on a Banach space, Argyros-Haydon space, Spaces of operators; tensor products; approximation properties, Banach module
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