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Session 4. Banach Spaces and Operator Theory with Applications
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The spectrum of the ball algebra of a Banach space |
Manuel Maestre, University of valencia, Spain
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In this talk we report on recent work done with different authors:
Richard Aron, Daniel Carando, Ted Gamelin, Domingo García and
Silvia Lasalle, on the study of some properties of the set of
homomorphisms of the Banach algebra \(A_u(B_X)\) of complex-valued
functions defined on \(B_X\), the open unit ball of a complex Banach
space \(X\) that are analytic and uniformly continuous on that
ball. We consider the case when \(X\) is a Banach space with an
unconditional shrinking basis. But we will concentrate in properties
of the ball algebra of some classical Banach spaces as \(c_0\),
\(\ell_1\)
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References- R. M. Aron, D. Carando, T. Gamelin, S. Lassalle and
M. Maestre, Cluster values of analytic functions on a Banach
space , Math. Annalen, 2012, 353 n.2, (2012) 293--303.
- R. M. Aron, D. Carando, S. Lassalle and M. Maestre,
Cluster values of holomorphic functions of bounded type , to
appear in Trans. Amer. Math. Soc.
- R. M. Aron, D. García and M. Maestre,
Embedding disks in the ball algebra of a Banach space, preprint
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