Complex convexity in Lebesgue-Bochner Function Spaces

Dowling, Patrick; Hu, Zhibao; Mupasiri, Douglas

doi:10.1090/S0002-9947-96-01508-5

Complex convexity in Lebesgue-Bochner Function Spaces
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by Patrick N. Dowling, Zhibao Hu and Douglas Mupasiri PDF

Trans. Amer. Math. Soc. 348 (1996), 127-139 Request permission

Abstract:

Complex geometric properties of continuously quasi-normed spaces are introduced and their relationship to their analogues in real Banach spaces is discussed. It is shown that these properties lift from a continuously quasi-normed space $X$ to $L^p(\mu , X)$, for $0 < p < \infty$. Local versions of these properties and results are also considered.

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