Holomorphic germs on Banach spaces
Annales de l'Institut Fourier, Volume 21 (1971) no. 3, p. 107-141

Let E and F be two complex Banach spaces, U a nonempty subset of E and K a compact subset of E. The concept of holomorphy type θ between E and F, and the natural locally convex topology 𝒯 ω,θ on the vector space θ (U,F) of all holomorphic mappings of a given holomorphy type θ from U to F were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space θ (K,F) of all germs of holomorphic mappings into F around K of a given holomorphy type θ, and study its interplay with θ (U,F) and some other properties of the topology 𝒯 ω,θ .

Soient E et F des espaces de Banach complexes, U un ouvert non-vide de E et K un compact de E. La notion de type d’holomorphie θ de E dans F et la topologie localement convexe naturelle 𝒯 ω,θ sur l’espace vectoriel θ (U,F) de toutes les applications holomorphes de U dans F, d’un type d’holomorphie donné θ, ont été considérées d’abord par L. Nachbin. C’est le motif pour lequel nous introduisons l’espace localement convexe θ (K,F) de tous les germes d’applications holomorphes autour de K dans F, d’un type d’holomorphie donné θ, en étudiant ses rapports avec θ (U,F), et quelques unes des propriétés de la topologie 𝒯 ω,θ .

@article{AIF_1971__21_3_107_0,
     author = {Chae Soo Bong},
     title = {Holomorphic germs on Banach spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {21},
     number = {3},
     year = {1971},
     pages = {107-141},
     doi = {10.5802/aif.381},
     zbl = {0222.46018},
     mrnumber = {49 \#9627},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1971__21_3_107_0}
}
Chae Soo Bong. Holomorphic germs on Banach spaces. Annales de l'Institut Fourier, Volume 21 (1971) no. 3, pp. 107-141. doi : 10.5802/aif.381. http://www.numdam.org/item/AIF_1971__21_3_107_0/

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