Some convexity properties in direct integrals and Köthe-Bochner spaces

2017/09/27 by Jan-David Hardtke, Hardtke, Jan-David · 1 citation
Mathematics · Computer Science · #Advanced Banach Space Theory #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1709.09532

Abstract

The notion of direct integrals introduced by Haydon, Levy and Raynaud in 1991 is a generalisation of the well-known concept of Köthe-Bochner spaces of vector-valued functions (using a family of target spaces instead of just one space). Here we will discuss some classical geometric properties like strict convexity, local uniform convexity and uniform convexity in direct integrals. We will also consider strongly convex and very convex Köthe-Bochner spaces.

Cited by

• Optimal Hardy-weights for the Finsler p-Dirichlet integral with a potential

Related

• Integrals with values in Banach spaces and locally convex spaces
• Strong vector valued integrals
• Convexity, plurisubharmonicity and the strong maximum modulus principle in Banach spaces
• A simple proof for the convexity of the Choquet integral
• Norm Estimates for the Difference Between Bochner's Integral and the Convex Combination of Function's Values