Timeline for What are the right categories of finite-dimensional Banach spaces?
Current License: CC BY-SA 2.5
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| Nov 19, 2009 at 16:41 | comment | added | Terry Tao | Well, you can take ultralimits of morphisms also. A bunch of uniformly bounded linear transformations $T_i: E_i \to F_i$ induces a bounded linear transformation $T: \ell^\infty(I,E_i)/N_U \to \ell^\infty(I,F_i)/N_U$. This seems to give the right category if one wants dimension-independent bounds. If instead one wants (say) bounds that are polynomial on the dimension, one replaces "bounded" by "growing polynomial in the dimension" throughout, etc. | |
| Nov 19, 2009 at 16:32 | history | answered | Matthew Daws | CC BY-SA 2.5 |