• Seán Dineen
Part of the Springer Monographs in Mathematics book series (SMM)


Multilinear mappings, tensor products, restrictions to finite dimensional spaces and differential calculus may all be used to define polynomials over infinite dimensional spaces. All of these are useful, none should be neglected and, indeed, the different possible approaches and interpretations add to the richness of the subject. We adopt an integrated approach to the development of polynomials using multilinear mappings and tensor products. The philosophy of tensor products is easily stated: to exchange polynomial functions on a given space with simpler (linear) functions on a (possibly) more complicated space.


Banach Space Convex Space Normed Linear Space Bounded Subset Finite Dimensional Subspace 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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General References

  1. Banach space theory: S. Banach [83], A. Defant-K. Floret [258], J. Diestel [270], J. Diestel-H. Jarchow-A. Tonge [271], J. Diestel-J.J. Uhl, Jr. [272]. N. Dunford-J. Schwartz [337], S. Guerre-Delabrière [420], E. Hille [451], R.B. Holmes [461], J. Lindenstrauss-L. Tzafriri [555, 556].Google Scholar
  2. Locally convex spaces: H. Goldman [391], A. Grothendieck [414, 415, 416], J. Horváth [467], H. Jarchow [480], G. Köthe [522, 523], P. Pérez Carreras-J. Bonet [720], A. Pietsch [724], H.H. Schaefer [770].Google Scholar
  3. Several complex variables: L. Hörmander [466], J. Mujica [651].Google Scholar

Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Seán Dineen
    • 1
  1. 1.Department of MathematicsUniversity College DublinBelfield Dublin 4Ireland

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