Commuting holomorphic maps on the spectral unit ball

2009 ◽  
Vol 41 (1) ◽  
pp. 57-62 ◽  
Author(s):  
C. Costara
Keyword(s):  
Unit Ball ◽  
Holomorphic Maps ◽  
Spectral Unit Ball

scholarly journals On the Singular Loci and the Images of Proper Holomorphic Maps From Pseudoellipsoids

2015 ◽  
Vol 117 (2) ◽  
pp. 170
Author(s):  
Cristina Giannotti ◽  
Andrea Spiro
Keyword(s):  
Unit Ball ◽  
Holomorphic Maps ◽  
Proper Holomorphic Maps ◽  
Singular Loci

We prove a generalisation of Rudin's theorem on proper holomorphic maps from the unit ball to the case of proper holomorphic maps from pseudoellipsoids.

Holomorphic Self-Maps of the Spectral unit Ball

1991 ◽  
Vol 23 (3) ◽  
pp. 256-262 ◽  
Author(s):  
T. J. Ransford ◽  
M. C. White
Keyword(s):  
Unit Ball ◽  
Spectral Unit Ball

scholarly journals A local form for the automorphisms of the spectral unit ball

2008 ◽  
Vol 59 (3) ◽  
pp. 321-324 ◽  
Author(s):  
Pascal J. Thomas
Keyword(s):  
Unit Ball ◽  
Local Form ◽  
Spectral Unit Ball

scholarly journals Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jorge J. Garcés ◽  
Antonio M. Peralta ◽  
Daniele Puglisi ◽  
María Isabel Ramírez
Keyword(s):  
Unit Ball ◽  
Taylor Series ◽  
Holomorphic Mapping ◽  
Invertible Element ◽  
Holomorphic Mappings ◽  
Open Unit ◽  
Holomorphic Maps ◽  
Open Unit Ball ◽  
C Algebras ◽  
Orthogonally Additive

We study holomorphic maps between C*-algebrasAandB, whenf:BA(0,ϱ)→Bis a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ballU=BA(0,δ). If we assume thatfis orthogonality preserving and orthogonally additive onAsa∩Uandf(U)contains an invertible element inB, then there exist a sequence(hn)inB**and Jordan*-homomorphismsΘ,Θ~:M(A)→B**such thatf(x)=∑n=1∞hnΘ~(an)=∑n=1∞Θ(an)hnuniformly ina∈U. WhenBis abelian, the hypothesis ofBbeing unital andf(U)∩inv(B)≠∅can be relaxed to get the same statement.

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