The problem of existence and uniqueness of greatest lower bound (glb) and l
east upper bound (lub) of a set in group induced cone (GIC) ordering is dis
cussed. Explicit formula for the gib is given. The results are applied to o
btain the best possible upper bound in GIC ordering for values of linear an
d nonnegative linear maps. (C) 2000 Elsevier Science Inc. All rights reserv
ed.