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New Banach space properties of the disc algebra and \(H^{\infty}\). (English) Zbl 0574.46039

The purpose of this paper is to prove some new linear properties of the disc algebra A and the space \(H^{\infty}\) of bounded analytic functions on the unit disc. The numerous results established in this major work involve absolutely summing operators, cotype, finite rank projections, the Dunford-Pettis property and weak completeness. Moreover, the author solves several of the main problems that appeared in A. Pełczynski’s notes [CBMS Reg. Conf., Kent State Univ. 1976, Reg. Conf. Ser. Math. 30 (1977; Zbl 0384.46015)].
Reviewer: G.Csordas

MSC:

46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
46B20 Geometry and structure of normed linear spaces
46J10 Banach algebras of continuous functions, function algebras

Citations:

Zbl 0384.46015
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