A fibered description of the vector-valued spectrum. (English) Zbl 1523.46037
Summary: For Banach spaces \(X\) and \(Y\) we study the vector-valued spectrum \(\mathcal{M}_\infty(B_X,B_Y)\), that is the set of non null algebra homomorphisms from \(\mathcal{H}^\infty(B_X)\) to \(\mathcal{H}^\infty(B_Y)\), which is naturally projected onto the closed unit ball of \(\mathcal{H}^\infty(B_Y,X^{\ast\ast})\). The aim of this article is to describe the fibers defined by this projection, searching for analytic balls and considering Gleason parts.
MSC:
| 46G20 | Infinite-dimensional holomorphy |
| 46J15 | Banach algebras of differentiable or analytic functions, \(H^p\)-spaces |
| 47A10 | Spectrum, resolvent |
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