Multiplication operators on L_p spaces and homological triviality of respective category of modules

2013/09/19 by N. T. Nemesh, Nemesh, Norbert
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1309.4974

Abstract

We give complete characterisation of topologically injective (bounded below), topologically surjective (open mapping), isometric and coisometric (quotient mapping) multiplication operators between L_p spaces defined on different σ-finite measure spaces. We prove that all such operators invertible from the left or from the right. As the consequence we prove that all objects of the category of L_p spaces considered as left Banach modules over algebra of bounded measurable functions are metrically, extremelly and relatively projective, injective and flat.

Related

• Topological transivity and mixing of the composition operators
• Projective and injective tensor products of Banach L⁰-modules
• Minimal and maximal p-operator space structures
• Multiplication operators on vector-valued function spaces
• Topological structure of the space of composition operators on L^∞ of an unbounded, locally finite metric space