Ferrera Cuesta, Juan2023-06-202023-06-201998G. Beer, Converyence of coratinuona linear functionals arad their level seis. Arch. Math., 52, 1989, p. 482-491. G. Beer, Topologies on closed arad elosed convea’ seta. Kluwer Academic Publishers, Dordrecht, 1993. J.M. Borwein, 5. Fitzpatrick, Mosco convergence and tite Kadec properly. Proc. A.M.S., 106, 1989, p. 843-851. J.M. Borwein, J. Vanderwerff, Dual Kadec-Klee norrns and tiae relationsitipa betunee» Wijsrnan, slice arad Mosco convergence. Preprint. J. Ferrera, Convergence of potynornial level seta. Trans. Amer. Math. Soc. (To appear) C. Kuratowski, Topology. New York 1966 J. Llavona, Approa’imation of continuously differenliable funcliona.. North Holland Math. Studies (130) 1986. U. Mosco, Convergence of convea’ seta arad solulioras of variational iraequalities. Adv. in Math., 3,1971, p. 510-585. Mujica, Complez analysis ira Banach spaces. North Holland Math. Studies (120) 1986. M. Tsukada, Convergerace of tite besí approzimalions ira a srnootit Baraacit apace. 3. Approx. Theory, 40, 1984, p.30l-309. R Wijsman, Coravergence of sequences of coravea’ seis, coites and furacliona IL Trans. Amer. Math. Soc. 123, 1966, p. 32-45.1139-1138https://hdl.handle.net/20.500.14352/58704In this paper we give a characterization of uniform convergence on weakly compact sets, for sequences of homogeneous polynomials in terms of the Mosco convergence of their level sets. The result is partially extended for holomorphic functions. Finally we study the relationship with other convergences.engjournal articlehttp://www.mat.ucm.es/serv/revmat/vol11-1/vol11-1b.pdfhttp://www.mat.ucm.es/restricted access517.98Banach spaces.Análisis funcional y teoría de operadores