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Characterizations of norm--parallelism in spaces of continuous functions. (arXiv:1807.03780v1 [math.FA])
来源于:arXiv
In this paper, we consider the characterization of norm--parallelism problem
in some classical Banach spaces. In particular, for two continuous functions
$f, g$ on a compact Hausdorff space $K$, we show that $f$ is norm--parallel to
$g$ if and only if there exists a probability measure (i.e. positive and of
full measure equal to $1$) $\mu$ with its support contained in the norm
attaining set $\{x\in K: \, |f(x)| = \|f\|\}$ such that $\big|\int_K
\overline{f(x)}g(x)d\mu(x)\big| = \|f\|\,\|g\|$. 查看全文>>