Revistes Catalanes amb Accés Obert (RACO)

Linear topological invariants of spaces of holomorphic functions in infinite dimension

N. Minh Ha, L. M. Hai


It is shown that if $E$ is a Frechet space with the strong dual $E^*$ then $H_b(E^*)$, the space of holomorphic functions on $E^*$ which are bounded on every bounded set in $E^*$, has the property $(DN)$ when $E\in (DN)$ and that $H_b(E^*)\in(\Omega)$ when $E\in (\Omega)$ and either $E^*$ has an absolute basis or $E$ is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals $J(V)$ consisting of holomorphic functions on $E^*$ which are equal to $0$ on $V$ in $H(E^*)$ for every nuclear Frechet space $E$ with $E\in (DN)\cap (\Omega)$ is stablished when $J(V)$ is finitely generated by continuous polynomials on $E^*$.

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