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Bounded weak continuity of homogeneous polynomials at the origin

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Abstract.

Given a Banach space E we study P w 0(n E), the space of all continuous n-homogeneous polynomials which are weakly continuous on bounded sets at the origin. We examine the coincidence of P w 0(n E) with P(n E), of P w 0(n E) with P w (n E) and of P(n E) with P w (n E) with particular interest as to when either of these coincidence for polynomials of degree n implies the corresponding coincidence for polynomials of lower degree.

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Authors and Affiliations

  1. Department of Mathematics, National University of Ireland, Galway, Galway, Ireland, , , , , , IE

    Christopher Boyd & R.A. Ryan

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  1. Christopher Boyd
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  2. R.A. Ryan
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Received: 17.7.1997; revised version received 2.4.1998.

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Boyd, C., Ryan, R. Bounded weak continuity of homogeneous polynomials at the origin. Arch. Math. 71, 211–218 (1998). https://doi.org/10.1007/s000130050254

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  • DOI: https://doi.org/10.1007/s000130050254

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