ABSTRACT

Definition 5.1. Let X and Y be vector spaces over the field K = R or C. A multivalued map (multimap) A : X → P(Y ) is is said to be a multivalued linear operator (MLO)(or linear relation) if:

i) A(x) +A(y) = A(x+ y), ∀x, y ∈ D(A), ii) A(λx) = λA(x), ∀λ ∈ K\{0}, ∀x ∈ D(A). The class of multivalued linear operators will be denoted by ML(X,Y ). We write

MLO(X,X) := MLO(X).