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A characterization of holomorphic germs on compact perfect sets

Graciela Carboni, Angel Rafael Larotonda (2004)

Commentationes Mathematicae Universitatis Carolinae

Let K ⊆ ℂ be a perfect compact set, E a quasi-complete locally convex space over ℂ and f : K → E a map. In this note we give a necessary and sufficient condition — in terms of differential quotients — for f to have a holomorphic extension on a neighborhood of K .

A classification for real and complex finite dimensional ℱ * -algebras

Mauro Meschiari (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

La presente Nota contiene una lista di J ⋆ -algebre reali di dimensione finita ed una lista di J ⋆ -algebre complesse di dimensione finita tali che: 1) due elementi distinti di ogni lista non sono mai J ⋆ -isomorfi; 2) ogni J ⋆ -algebra di dimensione finita reale (complessa) è J ⋆ —isomorfa su 𝐑 (su 𝐂 ) alla somma diretta, finita, di J ⋆ -algebre reali (complesse) elencate nella lista. In altre parole, diamo qui una classificazione completa delle J ⋆ —algebre reali e delle J ⋆ -algebre complesse di dimensione finita. Nel...

A note on Alexander's theorem.

Le Mau Hai, Nguyen Van Khue, Sičiak, Józef (2005)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

A stronger Dunford-Pettis property

H. Carrión, P. Galindo, M. L. Lourenço (2008)

Studia Mathematica

We discuss a strong version of the Dunford-Pettis property, earlier named (DP*) property, which is shared by both ℓ₁ and ℓ ∞ . It is equivalent to the Dunford-Pettis property plus the fact that every quotient map onto c₀ is completely continuous. Other weak sequential continuity results on polynomials and analytic mappings related to the (DP*) property are shown.

Analytic cohomology of complete intersections in a Banach space

Imre Patyi (2004)

Annales de l’institut Fourier

Let X be a Banach space with a countable unconditional basis (e.g., X = ℓ 2 ), Ω ⊂ X an open set and f 1 , ... , f k complex-valued holomorphic functions on Ω , such that the Fréchet differentials d f 1 ( x ) , ... , d f k ( x ) are linearly independant over ℂ at each x ∈ Ω . We suppose that M = { x ∈ Ω : f 1 ( x ) = ... = f k ( x ) = 0 } is a complete intersection and we consider a holomorphic Banach vector bundle E → M . If I (resp. 𝒪 E ) denote the ideal of germs of holomorphic functions on Ω that vanish on M (resp. the sheaf of germs of holomorphic sections of E ), then the sheaf cohomology groups H q ( Ω , I ) , H q ( M , 𝒪 E ) vanish...

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