@article{10902/32430,
year = {2023},
month = {4},
url = {https://hdl.handle.net/10902/32430},
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.},
organization = {The research of the first and third authors was supported in part by MINCIN project PID2019-103961GB.
The research of the first author was supported in part by Junta de Extremadura project IB20038. The
research of the second author was supported by FAPESP grants (2016/25574-8), (2018/18593-1) and
(2019/23669-0). The research of the fourth author was partially supported by project
FEDER-UCA18-108415 funded by 2014–2020 ERDF Operational Programme and by the Department of
Economy, Knowledge, Business and University of the Regional Government of Andalucia.},
publisher = {Springer},
publisher = {Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 2023, 117(2), 56},
title = {On symplectic Banach spaces},
author = {Fernández Castillo, Jesús María and Cuellar, Wilson and González Ortiz, Manuel and Pino, Raúl},
}