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Let be a p-convex () order continuous Banach function space over a positive finite measure . We characterize the subspaces of which can be found simultaneously in and a suitable space, where is a positive finite measure related to the representation of as an space of a vector measure . We provide in this way new tools to analyze the strict singularity of the inclusion of in such an space. No rearrangement invariant type restrictions on are required. J.M. Calabuig was supported by Ministerio de Economia y Competitividad (project MTM2011-23164) (Spain). J. Rodriguez was supported by Ministerio de Economia y Competitividad (project MTM2011-25377) (Spain). E. A. Sanchez-Perez was supported by Ministerio de Economia y Competitividad (project MTM2009-14483-C02-02) (Spain). Calabuig Rodriguez, JM.; Rodríguez Ruiz, J.; Sánchez Pérez, EA. (2013). Strongly embedded subspaces of p-convex Banach function spaces. Positivity. 17(3):775-791. doi:10.1007/s11117-012-0204-6 Astashkin, S.V., Hernández, F.L., Semenov, E.M.: Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces. Studia Math. 193(3), 269–283 (2009) Cobos, F., Pustylnik, E.: On strictly singular and strictly cosingular embeddings between Banach lattices of functions. Math. Proc. Cambridge Philos. Soc. 133(1), 183–190 (2002) Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1995) Diestel, J., Uhl J.J. Jr., Vector measures. American Mathematical Society, Providence (1977) (With a foreword by B. J. Pettis, Mathematical Surveys, No. 15) Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., Sánchez-Pérez, E.A.: Vector measure Maurey-Rosenthal-type factorizations and $$l$$ -sums of $$L^1$$ -spaces. J. Funct. Anal. 220(2), 460–485 (2005) Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., Sánchez-Pérez, E.A.: Spaces of $$p$$ -integrable functions with respect to a vector measure. Positivity 10(1), 1–16 (2006) Figiel, T., Johnson, W.B., Tzafriri, L.: On Banach lattices and spaces having local unconditional structure, with applications to Lorentz function spaces, J. Approx. Theory 13:395–412 (1975) (Collection of articles dedicated to Lorentz, G.G. on the occasion of his sixty-fifth birthday, IV) Flores, J., Hernández, F.L., Kalton, N.J., Tradacete, P.: Characterizations of strictly singular operators on Banach lattices. J. Lond. Math. Soc. (2) 79(3), 612–630 (2009) Hernández, F.L., Novikov, S.Ya., Semenov, E.M.: Strictly singular embeddings between rearrangement invariant spaces, Positivity 7(no. 1–2), 119–124 (2003) [Positivity and its applications (Nijmegen, 2001)] Hernández, F.L., Sánchez, V.M., Semenov, E.M.: Disjoint strict singularity of inclusions between rearrangement invariant spaces. Studia Math. 144(3), 209–226 (2001) Hernández, F.L., Sánchez, V.M., Semenov, E.M.: Strictly singular and strictly co-singular inclusions between symmetric sequence spaces. J. Math. Anal. Appl. 291(2), 459–476 (2004) Hernández, F.L., Sánchez, V.M., Semenov, E.M.: Strictly singular inclusions into $$L^1+L^\infty $$ . Math. Z. 258(1), 87–106 (2008) Okada, S., Ricker, W.J., Sánchez-Pérez, E.A.: Optimal domain and integral extension of operators. In: Operator Theory: Advances and Applications. Acting in function spaces, vol. 180. Birkhäuser Verlag, Basel (2008) 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), 907–923 (2001)

Strongly embedded subspaces of p-convex Banach function spaces

Abstract