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- W3046344470 abstract "Let $X$ be a Banach space, $Sigma$ be a $sigma$-algebra, and $m:Sigmato X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski factorization procedure that there exist a reflexive Banach space $Y$, a vector measure $tilde{m}:Sigma to Y$ and an injective operator $J:Y to X$ such that $m$ factors as $m=Jcirc tilde{m}$. We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pelczýnski factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on $L_1(m)$ is weakly compact, then $L_1(m)$ is equal, up to equivalence of norms, to some $L_1(tilde m)$ where $Y$ is reflexive; here we prove that the above equality can be taken to be isometric." @default.
- W3046344470 created "2020-08-07" @default.
- W3046344470 creator A5026174074 @default.
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- W3046344470 date "2020-07-31" @default.
- W3046344470 modified "2023-09-27" @default.
- W3046344470 title "Isometric factorization of vector measures and applications to spaces of integrable functions" @default.
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