Infinite dimensional holomorphic non-extendability and algebraic genericity

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• 作者：Luis Bernal-Gonzá ; lez^a ; ^{lbernal@us.es" class="auth_mail" title="E-mail the corresponding author} ; Marí ; a del Carmen Calderó ; n-Moreno^a ; ^{mccm@us.es" class="auth_mail" title="E-mail the corresponding author} ; Juan Benigno Seoane-Sepú ; lveda^b ; ^{jseoane@ucm.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 46G20 ; secondary ; 15A03 ; 30B40 ; 30H50 ; 32D05 ; 46J10
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：513
• 期：Complete
• 页码：149-159
• 全文大小：349 K

文摘

In this note, the linear structure of the family H_e(G)$H_e(G)$ of holomorphic functions in a domain G of a complex Banach space that are not holomorphically continuable beyond the boundary of G   is analyzed. More particularly, we prove that H_e(G)$H_e(G)$ contains, except for zero, a closed (and a dense) vector space having maximal dimension, as well as a maximally generated free algebra. The results obtained complete a number of previous ones by several authors.