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- W1994369327 abstract "We show that any infinite compact Hausdorff space S is the continuous image of a totally disconnected compact Hausdorff space $Sâ$, having the same topological weight as S, by a map $varphi$ which admits a regular linear operator of averaging, i.e., a projection of norm one of $C(Sâ)$ onto ${varphi ^ circ }C(S)$, where ${varphi ^circ }:C(S) to C(Sâ)$ is the isometric embedding which takes $f in C(S)$ into $f circ varphi$. A corollary of this theorem is that if S is an absolute extensor for totally disconnected spaces, the space $Sâ$ can be taken to be the Cantor space ${{ 0,1} ^mathfrak {m}}$, where $mathfrak {m}$ is the topological weight of S. This generalizes a result due to Milutin and PeÅczyÅski. In addition, we show that for compact metric spaces S and T and any continuous surjection $varphi :S to T$, the operator $u:C(S) to C(T)$ is a regular averaging operator for $varphi$ if and only if u has a representation $uf(t) = smallint _0^1f(theta (t,x))$ for a suitable function $theta :T times [0,1] to S$." @default.
- W1994369327 created "2016-06-24" @default.
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- W1994369327 date "1970-02-01" @default.
- W1994369327 modified "2023-09-25" @default.
- W1994369327 title "On a lemma of Milutin concerning averaging operators in continuous function spaces" @default.
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- W1994369327 doi "https://doi.org/10.1090/s0002-9947-1970-0435921-2" @default.
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