Index

A0*, one-sided bipolar of set A, 135, 249

A*, one-sided polar of set A, 134, 249

AfF, vector space of afRne functions, 227

A°, polar of set A, 248

A°°, bipolar of set A, 249

Ax, half-ray generated by x, 37, 40

absolute polar of a set, 248

absolute value

of functional, 56

of operator, 54

of vector, 14

absorbing set, 33, 110, 244

additive function, 23, 184

additive mapping, 23, 184

adjoint operator, 148

Hilbert space, 109

affine function, 221, 227

afRne transformation, 231

Alaoglu-Bourbaki theorem, 248

algebraic dual, 205, 246

algebraic dual of a vector space, 31, 246

algebraic separating hyperplane theorem,

251

almost Archimedean cone, 12

almost Archimedean ordered vector space,

12

alternative

concave, 150

Farkas, 149

operator, 148

Stiemke, 149

wedge, 148

Ando's theorem, 66, 88, 91, 92

angle of an ice cream cone, 99

antisymmetry, 3

Archimedean cone, 11, 63, 119, 128

Archimedean ordered vector space, 11

Archimedean property, 11

arrangement generated by afRne functions,

235

arrangement of hyperplanes, 234

associative law, 178

atom, 39

axis of ice cream cone, 99

/3(L, Z/), strong topology on L, 251

/3(Z/,L), strong topology on L', 251

A°°, bipolar of set A, 249

[£], full hull of set B, 6

balanced set, 6, 244

Banach lattice, 85

Banach space, 253

ordered, 85

reflexive, 254

separable, 254

with the Levi property, 89

with the strong Levi property, 89

Banach-Steinhaus theorem, 254

base of cone, 39

pseudo, 200

basis

Hamel, 124

positive, 125

Yudin, 125

bilinear mapping, 247

bilinearity of a dual pair, 247

bipolar of a set, 249

bipolar theorem, 249

one-sided, 135, 249

Birkhoff's identity, 21

Birkhoff's inequalities, 21

Borel sets, 75

271