Multi-dimensional volumes and moduli of convexity in Banach spaces

DOI10.1007/BF01811725zbMath0472.46018MaRDI QIDQ1157747

S. H. Smith

Publication date: 1981

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

moduli of convexityDixmier's theorem on higher duals of non-reflexive spacesmodulus of rotunditymulti-dimensional volumesnearest-point maps

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Best approximation, Chebyshev systems (41A50) Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03)

Related Items

Banach spaces which are dual to \(k\)-uniformly convex spaces ⋮ k-uniform rotundity is equivalent to k-uniform convexity ⋮ \(k\)-uniform rotundity is equivalent to \(k\)-uniform convexity ⋮ Fixed point theorems of nonexpansive mappings on weakly compact sets ⋮ On \(k\)-rotundity and \(k\)-uniform rotundity in direct sums of normed spaces ⋮ Multidimensional moduli of convexity and rotundity in Banach spaces ⋮ GEOMETRIC AND FIXED POINT PROPERTIES IN PRODUCTS OF NORMED SPACES ⋮ \(k\)-\(\beta\) and \(k\)-nearly uniformly convex Banach spaces ⋮ Geometric constants concerning metric fixed point theory: Finite or infinite dimensional character ⋮ The locally \(k\)-uniformly extremely convex and midpoint locally \(k\)-uniformly extremely convex Banach spaces ⋮ Unnamed Item ⋮ Geometry of product spaces ⋮ A fixed point theorem on k-uniformly rotund spaces ⋮ Duaux transfinis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometrical properties determined by the higher duals of a Banach space
• Inner diameter, perimeter, and girth of spheres
• Reflexivity and the girth of spheres
• Sur un théorème de Banach
• Set functions associated with Lebesgue area
• Uniform convexity in factor and conjugate spaces
• A Representation Theorem for Bounded Convex Sets
• The $l^{n}_{1}$ problem and degrees of non-reflexivity (II)
• A Generalization of Uniformly Rotund Banach Spaces
• On the canonical projection of the third dual of a Banach space onto the first dual
• The $l^{n}_{1}$ problem and degrees of non-reflexivity
• On the moduli of convexity and smoothness
• TRANSFINITE DUALS OF BANACH SPACES AND ERGODIC SUPER-PROPERTIES EQUIVALENT TO SUPEREFLEXIVITY
• Geometric theory of Banach spaces. Part I. The theory of basis and minimal systems
• GEOMETRIC THEORY OF BANACH SPACES. PART II. GEOMETRY OF THE UNIT SPHERE
• The Equation L(E, X ∗ ∗ = L(E, X) ∗ ∗ and the Principle of Local Reflexivity