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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Products of polynomials and the geometry of Banach spaces
by
Christopher Boyd
University College Dublin, Belfield, Dublin 4
Coauthors: R.A. Ryan

Let E be a Banach space, k and l be positive integers and n=k+l. It is shown in [1] that given P in P(kE), Q in P(lE) then
||P||||Q|| <=  nn
kkll
 ||PQ||.
For l1 this estimate is sharp. If however E has nice geometric properties then it may be possible to improve on these estimates. Our estimates depend on E either having finite type or being uniformly convex. Improved estimates can also be obtained if the `approximate norming circles' of P and Q are far apart.

[1] Benítez C., Sarantopoulos Y. & Tonge A., Lower bounds for the norms of products of polynomials, Math. Proc. Cambridge Philos. Soc. 124, (1998), 395-408.

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Date received: April 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caei-86.