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- W1655944618 abstract "A mapping between Banach spaces is said to be polynomially continuous if its restriction to any bounded set is uniformly continuous for the weak polynomial topology. A Banach space $X$ has property (RP) if given two bounded sequences $(u_j), (v_j)subset X$, we have that $Q(u_j)-Q(v_j)rightarrow 0$ for every polynomial $Q$ on $X$ whenever $P(u_j-v_j)rightarrow 0$ for every polynomial $P$ on $X$; i.e., the restriction of every polynomial on $X$ to each bounded set is uniformly sequentially continuous for the weak polynomial topology. We show that property (RP) does not imply that every scalar valued polynomial on $X$ must be polynomially continuous." @default.
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- W1655944618 date "1997-01-01" @default.
- W1655944618 modified "2023-10-16" @default.
- W1655944618 title "Polynomial continuity on $ell _1$" @default.
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- W1655944618 doi "https://doi.org/10.1090/s0002-9939-97-03733-7" @default.
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