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A reflexive space of holomorphic functions in infinitely many variables. (English) Zbl 0536.46015

Let \(E=T^*\) be Tsirelson’s original Banach space, a reflexive Banach space with unconditional basis containing no copy of \(\ell_ p,c_ 0\), or \(\ell_ 1\). The authors prove that H(E), the space of holomorphic functions on E, endowed with the Nachbin topology \(\tau_{\omega}\) is reflexive. The method of proof is to show that for all n, the space \(P(^ nT^*)\) of continuous n-homogeneous polynomials is reflexive, and to accomplish this, the authors use a weak sequential continuity characterization of reflexity.

MSC:

46E10 Topological linear spaces of continuous, differentiable or analytic functions
32A30 Other generalizations of function theory of one complex variable
46B20 Geometry and structure of normed linear spaces
46B25 Classical Banach spaces in the general theory
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