On symplectic Banach spaces

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URI: https://hdl.handle.net/10902/32430
ISSN: 1578-7303
ISSN: 1579-1505
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Autoría
Fernández Castillo, Jesús María; Cuellar, Wilson; González Ortiz, ManuelAutoridad Unican; Pino, Raúl
Fecha
2023-04
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 2023, 117(2), 56
Editorial
Springer
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Palabras clave
Symplectic Banach space
Symplectic operator
Rochberg spaces
Kalton–Peck space
Hilbert space
Resumen/Abstract
We extend and generalize the result of Kalton and Swanson (Z₂ is a symplectic Banach space with no Lagrangian subspace) by showing that all higher order Rochgberg spaces R(n) are symplectic Banach spaces with no Lagrangian subspaces. The nontrivial symplectic structure on Rochberg spaces of even order is the one induced by the natural duality; while the nontrivial symplectic structure on Rochberg spaces of odd order requires perturbation with a complex structure.We will also study symplectic structures on general Banach spaces and, motivated by the unexpected appearance of complex structures, we introduce and study almost symplectic structures.
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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.Excepto si se señala otra cosa, la licencia del ítem se describe como This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.