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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

4 votes
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141 views

Dual spaces of Banach-valued $L^{p}$-spaces

Let $(\Omega,\mathcal{F},\mu)$ be a measure space (say complete and $\sigma$-finite, for simplicity). Furthermore, let $(X,\Vert\cdot\Vert_{X})$ be an arbitrary Banach space. I denote by $(L^{p}(\Omeg …