Abstract
We study the vector-valued spectrum $\mathcal {M}_{u,\infty }(B_{\ell _2},B_{\ell _2})$, which is the set of non-zero algebra homomorphisms from $\mathcal {A}_u(B_{\ell _2})$ (the algebra of uniformly continuous holomorphic functions on $B_{\ell _2}$) to
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