Complex convexity and the geometry of Banach spaces

DOI10.1017/S0305004100064446zbMath0611.46026MaRDI QIDQ3752083

Stephen Dilworth

Publication date: 1986

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

Banach latticesquasi-Banach spaceBanach-Mazur distanceanalytic Radon-Nikodym propertyunconditional convergenceuniform smoothnessgeometry of Banach spacescomplex uniform convexitycomplex interpolation paircomplex convexity

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Radon-Nikodým, Kre?n-Milman and related properties (46B22)

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Bishop-Phelps-Bollobás property for bilinear forms on spaces of continuous functions ⋮ Complex strict convexity of absolute norms on \(\mathbb {C}^n\) and direct sums of Banach spaces ⋮ The \(p\)-Bohr radius of a Banach space ⋮ Bohr and Rogosinski inequalities for operator valued holomorphic functions ⋮ Complex convexity in Lebesgue-Bochner Function Spaces ⋮ Interpolation between vector-valued Hardy spaces ⋮ Denseness of norm-attaining mappings on Banach spaces ⋮ Monotonicity and complex convexity in Banach lattices ⋮ Complex convexity and monotonicity in quasi-Banach lattices ⋮ Complex Interpolation and Convexity ⋮ Criteria for complex strongly extreme points of Musielak--Orlicz function spaces ⋮ Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals ⋮ Complex extreme points in Marcinkiewicz spaces ⋮ Orlicz norm estimates for eigenvalues of matrices

Cites Work

• The complex convexity of quasi-normed linear spaces
• On complex strictly convex spaces. I
• Projections onto Hilbertian subspaces of Banach spaces
• On complex strictly convex spaces. II
• c-convex Banach lattices
• Boundary properties of analytic and harmonic functions with values in Banach space
• Sous-espaces de dimension finie des espaces de Banach reticules
• Martingales with values in uniformly convex spaces
• Interpolation of Uniformly Convex Banach Spaces
• On Complex Strict and Uniform Convexity
• The Strong Maximum Modulus Theorem for Analytic Functions into a Banach Space