Characterizations of some operator spaces by relative adjoint operators Original Research Article

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))L(ℓ∞(A,X),c0(A,Z)) is equivalent to View the MathML sourcec0(A,LSOT(ℓ∞(A,X),Z)) in the sense of isometric isomorphism, where AA is an infinite set, XX, ZZ are Banach spaces and View the MathML sourceLSOT(X,Z) is the space L(X,Z)L(X,Z) endowed with the strong operator topology. Note that the vector-valued function spaces ℓ∞(A,X)ℓ∞(A,X) and c0(A,Z)c0(A,Z), defined in the prerequisites, are important generalizations of the classical Banach spaces ℓ∞ℓ∞and c0c0.