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 -