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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A symplectic Banach space with no Lagrangian subspaces
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by N. J. Kalton and R. C. Swanson PDF
Trans. Amer. Math. Soc. 273 (1982), 385-392 Request permission

Abstract:

In this paper we construct a symplectic Banach space $(X,\Omega )$ which does not split as a direct sum of closed isotropic subspaces. Thus, the question of whether every symplectic Banach space is isomorphic to one of the canonical form $Y \times {Y^ \ast }$ is settled in the negative. The proof also shows that $\mathfrak {L}(X)$ admits a nontrivial continuous homomorphism into $\mathfrak {L}(H)$ where $H$ is a Hilbert space.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 273 (1982), 385-392
  • MSC: Primary 58B20; Secondary 46B99
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0664050-6
  • MathSciNet review: 664050