Coordinate formalism on Hilbert manifolds
@article{Kryukov2001CoordinateFO,
title={Coordinate formalism on Hilbert manifolds},
author={Alexey A. Kryukov},
journal={arXiv: Mathematical Physics},
year={2001},
url={https://api.semanticscholar.org/CorpusID:515212}
}Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and infinite-dimensional manifolds deeply similar. In this context the infinite-dimensional counterparts of simple notions such as basis, dual basis, orthogonal basis, etc. are shown to be closely related to the choice of a model. It is also shown that in this formalism a single…
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