Seoane-Sepúlveda, Juan B.2023-06-202023-06-202007E. Abakumov and J. Gordon, Common hypercyclic vectors for multiples of backward shift, J. Funct. Anal. 200 (2003),no. 2, 494–504. R. M. Aron, J. B. Seoane-Sepulveda and A. Weber, Chaos on function spaces, Bull.Austral. Math. Soc. 71 (2005), no. 3,411–415. J. P. Bes, Invariant manifolds of hypercyclic vectors for the real scalar case, Proc. Amer.Math. Soc. 127 (1999), no.6, 1801–1804. G. Godefroy and J. H. Shapiro, Operators with dense,invariant, cyclic vector manifolds,J. Funct. Anal. 98 (1991), no. 2, 229–269. S. Grivaux, Construction of operators with prescribed behaviour, Arch. Math. (Basel)81 (2003), no. 3, 291–299. M. Gonzalez, F. Leon-Saavedra and A. Montes-Rodrıguez, Semi-Fredholm theory: hypercyclic and supercyclic subspaces,Proc. London Math. Soc. (3) 81 (2000), no. 1,169–189. F. Leon-Saavedra and A. Montes-Rodrıguez, Spectral theory and hypercyclic subspaces,Trans. Amer. Math. Soc. 353 (2001), no. 1, 247–267 (electronic). A. Montes-Rodr´ıguez, Banach spaces of hypercyclic vectors, Michigan Math. J. 43 (1996), no. 3, 419–436. A. Montes-Rodrıguez and H. N. Salas, Supercyclic subspaces: spectral theory and weighted shifts, Adv. Math. 163 (2001),no. 1, 74–134. Supercyclic subspaces, Bull. London Math. Soc. 35 (2003),no. 6, 721–737. S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17–22. H. N. Salas, A hypercyclic operator whose adjoint is also hypercyclic, Proc. Amer. Math.Soc. 112 (1991), no. 3, 765–770.0034-531810.2977/prims/1201011786https://hdl.handle.net/20.500.14352/50464We give an explicit construction of a dense infinite dimensional vector space of hypercyclic vectors for the weighted backward shift T-lambda (vertical bar lambda vertical bar > 1). We also develop a technique to construct common hypercyclic vectors for countable families of these operators. The techniques developed here do not rely on the Baire category theorem or any kind of existence proof, as do most approaches to this problem.engjournal articlehttp://www.kurims.kyoto-u.ac.jp/~prims/pdf/43-2/43-2-17.pdfrestricted access517.98Hypercyclic subspacesWeighted shiftCommon hypercyclic vectorsAnálisis funcional y teoría de operadores