TY - JOUR
T1 - Banach Algebras where the Singular Elements Are Removable Singularities
AU - Harris, Lawrence A.
PY - 2000/3/1
Y1 - 2000/3/1
N2 - Let A be a C*-algebra with identity and suppose A has real rank 0. 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 show that then the function has a holomorphic extension to the entire open unit ball of A. Further, we show that this does not hold when A = C(S), where S is any compact Hausdorff space that contains a homeomorphic image of the interval [0, 1].
AB - Let A be a C*-algebra with identity and suppose A has real rank 0. 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 show that then the function has a holomorphic extension to the entire open unit ball of A. Further, we show that this does not hold when A = C(S), where S is any compact Hausdorff space that contains a homeomorphic image of the interval [0, 1].
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U2 - 10.1006/jmaa.1999.6631
DO - 10.1006/jmaa.1999.6631
M3 - Article
AN - SCOPUS:0346676635
SN - 0022-247X
VL - 243
SP - 1
EP - 12
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -