Talk:Unconditional convergence

While the "equivalent definition" with the signs is clearly equivalent for series with values in the real numbers, I don't see any reason why it should be equivalent for Banach space valued series. Reference in the mathematical literature? (PlanetMath is not a reliable source.)

See [https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/xion-unconditional-convergence-in-topological-vector-spaces/CAFE825BDA900557FC85CB17B8AE4989 here] (or [https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CAFE825BDA900557FC85CB17B8AE4989/S0080454100008335a.pdf/xion_unconditional_convergence_in_topological_vector_spaces.pdf for the article]). 129.104.241.220 (talk) 01:29, 8 March 2025 (UTC)