POSITIVE OPERATORS

xviii List of Special Symbols
E δ Dedekind completion of E 101
E u Universal completion of E 126
〈E,E ′ 〉 Riesz dual system 173
E ⊕ F Direct sum of two Riesz spaces 21
E ⊗ F The vector space of finite rank operators 64
E(T ) Set of positive extensions of positive operator T 26
f ⊗ u Rank one operator 64
Ker(T ) Kernel of operator T 94
L(X, Y ) The B-space of continuous operators from X to Y 254, 274
L(E,F) The vector space of operators from E to F 10
Lb(E,F) The order bounded operators from E to F 12
Lc(E,F) The σ-order continuous operators from E to F 48
Ln(E,F) The order continuous operators from E to F 47
Lr(E,F) The regular operators from E to F 12
Ls(E,F) The singular operators from E to F 48
NT Null ideal of operator T 51
Orth(E) Orthomorphisms on E 117
Orth ∞ (E) Generalized orthomorphisms on E 132
pA Minkowski functional of A 138
Px Projection onto the band Bx 38
PB Projection onto the band B 36
Ring(T ) Ring ideal generated by operator T 330
·r r-norm 255
ST Simple component of operator T 80
Sol(A) Solid hull of set A 171
σ(E,E ′ ) Weak topology on E 145, 156
|σ|(E,E ′ ) Absolute weak topology on E 174
TA Smallest extension of operator T 25
Tc σ-order continuous component of operator T 48
Tn Order continuous component of operator T 48
Ts Singular component of operator T 48
T ′ Adjoint of operator T 153
τ(X, X ′ ) Mackey topology on X 151
|τ|(X, X ′ ) Absolute Mackey topology on X 173
U Closed unit ball of a Banach space 157
U ′ Closed unit ball of the dual space 157
U ′′ Closed unit ball of second dual 157
w Weak topology 145, 156