Characterizations of some operator spaces by relative adjoint operators

In this work, we introduce the notion of relative adjoint operators and characterize some operator spaces by this notion and by the results presented in [Y. Yilmaz, Structural properties of some function spaces, Nonlinear Anal. 59 (2004) 959-971]. Hence, for example, we prove that the operator space L(ℓ∞(A,X),c0(A,Z)) is equivalent to c0(A,LSOT(ℓ∞(A,X),Z)) in the sense of isometric isomorphism, where A is an infinite set, X, Z are Banach spaces and LSOT(X,Z) is the space L(X,Z) endowed with the strong operator topology. Note that the vector-valued function spaces ℓ∞(A,X) and c0(A,Z), defined in the prerequisites, are important generalizations of the classical Banach spaces ℓ∞and c0.