Motivated by the well known Kadec-Pełczynski disjointification theorem, we undertake an analysis of the supports of non-zero functions in strongly embedded subspaces of Banach functions spaces. The main aim is to isolate those properties that bring additional information on strongly embedded subspaces. This is the case of the support localization property, which is a necessary condition fulfilled by all strongly embedded subspaces. Several examples that involve Rademacher functions, the Volterra operator, Lorentz spaces or Orlicz spaces are provided.
Blasco, O., Calabuig, J. M. and Sánchez Pérez, E. A., p-variations of vector measures with respect to vector measures and integral representation of operators, Banach J. Math. Anal., 9, 1 (2015), 273–285.
Calabuig, J. M., Rodríguez, J. and Sánchez Pérez, E. A., Strongly embedded subspaces of p-convex Banach function spaces, Positivity, 17(3) (2013), 775–791.
Carothers, N. L. and Dilworth, S. J., Subspaces of Lp;q, Proc. Am. Math. Soc., 104, 2 (1988), 537–545.
Diestel, J. and Uhl, J. J., Vector Measures, Math. Surveys, vol. 15, Amer. Math. Soc., Providence, RI, 1977.
Fernández, A., Mayoral, F., Naranjo, F., Sáez, C. and Sánchez-Pérez, E. A., Spaces of p-integrable functions with respect to a vector measure, Positivity, 10 (2006), 1–16.
Figiel, T., Johnson, W. B. and Tzafriri, L., On Banach lattices and spaces having local unconditional structure with applications to Lorentz funtion spaces, J. Approx. Theory, 13 (1975), 395–412.
Flores, J., Hernández, F. L., Kalton, N. J. and Tradacete, P., Characterizations of strictly singular operators on Banach lattices, J. London Math. Soc., (2) 79 (2009), 612–630.
Flores, J., Hernández, F. L., Semenov, E. M. and Tradacete, P., Strictly singular and power-compact operators on Banach lattices, Israel J. Math., 188, 1 (2012), 323–352.
Kadec, I. and Pełczynski, A., Bases, Lacunary sequences and complemented subspaces in the spaces Lp, Studia Math., 21 (1962), 161–176.
Kalton, N. J. , Banach spaces embedded into L0, Israel J. Math., 52, (1985), 305–319.
Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces, II, Springer, Berlin, 1996.
Novikov, S. Ya. , Singularities of embedding operators between symmetric function spaces on [0, 1], Math. Notes, 62 (4) (1997), 457–468.
Okada, S., Ricker, W. J. and Sánchez Pérez, E. A., Optimal domain and integral extension of operators acting in function spaces, Operator Theory: Advances and Applications, 180. Birkhäuser Verlag, Basel, 2008.
Okada, S., Ricker, W. J. and Sánchez Pérez, E. A., Lattice copies of c0 and ℓ1 in spaces of integrable functions for a vector measure, Dissertationes Mathe-maticae, 500 (2014), 66.
Rodin, V. A. and Semyonov, E. M., Rademacher series in symmetric spaces, Anal. Math., 1(2) (1975), 161–176.
Sánchez Pérez, E. A. , Compactness arguments for spaces of p-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces, Illinois J. Math., 45 3 (2001), 907–923.
Tradacete, P. , Subspace structure of Lorentz Lp,q spaces and strictly singular operators, J. Math. Anal. Appl., 367 1 (2010), 98–107.