In this dissertation, we consider the characterization of norm–parallelism problem in some classical Banach spaces. In particular, for two continuous functionsf , g on a compact Hausdorff space K, we show that f is norm–parallel to if andonly if there exists a probability measure (i.e., positive and of full measure equal to1 ) µ with its support contained in the norm-attaining set {x ∈ K : |f(x)| = ∥f∥}such that ∫K f(x)g(x)dµ(x) = ∥f∥∥g∥.
OTHER VARIANT TITLES
Variant Title
Characterizations of norm-parallelism in spaces of continuous functions