Aron, Richard M.; Galindo, Pablo Weakly compact multilinear mappings. (English) Zbl 0901.46038 Proc. Edinb. Math. Soc., II. Ser. 40, No. 1, 181-192 (1997). Summary: The notion of Arens regularity of a bilinear form on a Banach space \(E\) is extended to continuous \(m\)-linear forms, in such a way that the natural associated linear mappings, \(E\to{\mathcal L}({}^{m-1}E)\) and \((m-1)\)-linear mappings \(E\times \dots\times E\to E'\), are all weakly compact. Among other applications, polynomials whose first derivative is weakly compact are characterized. Cited in 15 Documents MSC: 46G20 Infinite-dimensional holomorphy 46B20 Geometry and structure of normed linear spaces Keywords:Arens regularity; continuous \(m\)-linear forms; polynomials whose first derivative is weakly compact PDFBibTeX XMLCite \textit{R. M. Aron} and \textit{P. Galindo}, Proc. Edinb. Math. Soc., II. Ser. 40, No. 1, 181--192 (1997; Zbl 0901.46038) Full Text: DOI References: [1] Aron, Bull. Soc. Math. France 106 pp 3– (1978) [2] Aron, Bull. Austral. Math. Soc. 52 pp 475– (1995) [3] DOI: 10.2307/2031695 · Zbl 0044.32601 · doi:10.2307/2031695 [4] DOI: 10.2307/2046674 · Zbl 0635.46044 · doi:10.2307/2046674 [5] DOI: 10.1216/rmjm/1181072626 · Zbl 0779.46034 · doi:10.1216/rmjm/1181072626 [6] Ryan, Pacific J. Math. 131 pp 179– (1988) · Zbl 0605.46038 · doi:10.2140/pjm.1988.131.179 [7] Pelczynski, Bull. Acad. Polonaise Sc. 11 pp 371– (1963) [8] Jarchow, Locally Convex Spaces (1981) · doi:10.1007/978-3-322-90559-8 [9] DOI: 10.1007/BF02772998 · Zbl 0819.46006 · doi:10.1007/BF02772998 [10] DOI: 10.1016/S0304-0208(08)72340-5 · doi:10.1016/S0304-0208(08)72340-5 [11] DOI: 10.1016/0022-1236(83)90081-2 · Zbl 0517.46019 · doi:10.1016/0022-1236(83)90081-2 [12] DOI: 10.1090/S0002-9947-96-01553-X · Zbl 0844.46024 · doi:10.1090/S0002-9947-96-01553-X [13] Diestel, Sequences and series in Banach spaces 92 (1984) · doi:10.1007/978-1-4612-5200-9 [14] Aron, J. Reine Angew. Math. 415 pp 51– (1991) [15] DOI: 10.2307/2044483 · Zbl 0536.46015 · doi:10.2307/2044483 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.