Removable singularities in C*-algebras of real rank zero

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• 作者：Lawrence A. Harris ^{larry@ms.uky.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Infinite dimensional holomorphy ; Weak (FU)
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1390-1393
• 全文大小：217 K

文摘

Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16000871&_mathId=si1.gif&_user=111111111&_pii=S0022247X16000871&_rdoc=1&_issn=0022247X&md5=42ba3cc16c0b3aa895bfadad11c2c28a" title="Click to view the MathML source">Aclass="mathContainer hidden">class="mathCode">$\mathfrak{A}$ be a C*-algebra with identity and real rank zero. Suppose a complex-valued function is holomorphic and bounded on the intersection of the open unit ball of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16000871&_mathId=si1.gif&_user=111111111&_pii=S0022247X16000871&_rdoc=1&_issn=0022247X&md5=42ba3cc16c0b3aa895bfadad11c2c28a" title="Click to view the MathML source">Aclass="mathContainer hidden">class="mathCode">$\mathfrak{A}$ and the identity component of the set of invertible elements of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16000871&_mathId=si1.gif&_user=111111111&_pii=S0022247X16000871&_rdoc=1&_issn=0022247X&md5=42ba3cc16c0b3aa895bfadad11c2c28a" title="Click to view the MathML source">Aclass="mathContainer hidden">class="mathCode">$\mathfrak{A}$. We give a short transparent proof that the function has a holomorphic extension to the entire open unit ball of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16000871&_mathId=si1.gif&_user=111111111&_pii=S0022247X16000871&_rdoc=1&_issn=0022247X&md5=42ba3cc16c0b3aa895bfadad11c2c28a" title="Click to view the MathML source">Aclass="mathContainer hidden">class="mathCode">$\mathfrak{A}$. The author previously deduced this from a more general fact about Banach algebras.