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 mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304815&_mathId=si1.gif&_user=111111111&_pii=S0024379516304815&_rdoc=1&_issn=00243795&md5=da69f19909935b4c4da2c99d911f16d4" title="Click to view the MathML source">H_e(G)mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><msub><mrow><mi>Hmi>mrow><mrow><mi>emi>mrow>msub><mo stretchy="false">(mo><mi>Gmi><mo stretchy="false">)mo>math> of holomorphic functions in a domain m>Gm> of a complex Banach space that are not holomorphically continuable beyond the boundary of m>G  m> is analyzed. More particularly, we prove that mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304815&_mathId=si1.gif&_user=111111111&_pii=S0024379516304815&_rdoc=1&_issn=00243795&md5=da69f19909935b4c4da2c99d911f16d4" title="Click to view the MathML source">H_e(G)mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><msub><mrow><mi>Hmi>mrow><mrow><mi>emi>mrow>msub><mo stretchy="false">(mo><mi>Gmi><mo stretchy="false">)mo>math> 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.