Removable singularities in C*-algebras of real rank zero

Lawrence A. Harris

doi:10.1016/j.jmaa.2016.01.053

Removable singularities in C*-algebras of real rank zero

Lawrence A. Harris

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let 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 A and the identity component of the set of invertible elements of A. We give a short transparent proof that the function has a holomorphic extension to the entire open unit ball of A. The author previously deduced this from a more general fact about Banach algebras.

Original language	English
Pages (from-to)	1390-1393
Number of pages	4
Journal	Journal of Mathematical Analysis and Applications
Volume	445
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.01.053
State	Published - Jan 15 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

Infinite dimensional holomorphy
Weak (FU)

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2016.01.053

Cite this

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title = "Removable singularities in C*-algebras of real rank zero",

abstract = "Let 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 A and the identity component of the set of invertible elements of A. We give a short transparent proof that the function has a holomorphic extension to the entire open unit ball of A. The author previously deduced this from a more general fact about Banach algebras.",

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N2 - Let 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 A and the identity component of the set of invertible elements of A. We give a short transparent proof that the function has a holomorphic extension to the entire open unit ball of A. The author previously deduced this from a more general fact about Banach algebras.

AB - Let 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 A and the identity component of the set of invertible elements of A. We give a short transparent proof that the function has a holomorphic extension to the entire open unit ball of A. The author previously deduced this from a more general fact about Banach algebras.

KW - Infinite dimensional holomorphy

KW - Weak (FU)

UR - https://www.scopus.com/pages/publications/84960154730

UR - https://www.scopus.com/pages/publications/84960154730#tab=citedBy

U2 - 10.1016/j.jmaa.2016.01.053

DO - 10.1016/j.jmaa.2016.01.053

M3 - Article

AN - SCOPUS:84960154730

SN - 0022-247X

VL - 445

SP - 1390

EP - 1393

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Removable singularities in C*-algebras of real rank zero

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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