文摘
In this note, the linear structure of the family class="mathmlsrc">class="formulatext 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">He(G)class="mathContainer hidden">class="mathCode"> 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 class="mathmlsrc">class="formulatext 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">He(G)class="mathContainer hidden">class="mathCode"> 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.