Quantitative factorization of weakly compact, Rosenthal, and $\xi$-Banach-Saks operators


  • Kevin Beanland
  • Ryan M. Causey




We prove quantitative factorization results for several classes of operators, including weakly compact, Rosenthal, and ξ-Banach-Saks operators.


Androulakis, G., Dodos, P., Sirotkin, G., and Troitsky, V. G., Classes of strictly singular operators and their products, Israel J. Math. 169 (2009), 221–250. https://doi.org/10.1007/s11856-009-0010-4

Argyros, S. A., Mercourakis, S., and Tsarpalias, A., Convex unconditionality and summability of weakly null sequences, Israel J. Math. 107 (1998), 157–193. https://doi.org/10.1007/BF02764008

Beanland, K., Causey, R. M., Freeman, D., and Wallis, B., Classes of operators determined by ordinal indices, J. Funct. Anal. 271 (2016), no. 6, 1691–1746. https://doi.org/10.1016/j.jfa.2016.06.015

Beanland, K. and Freeman, D., Ordinal ranks on weakly compact and Rosenthal operators, Extracta Math. 26 (2011), no. 2, 173–194.

Beanland, K. and Freeman, D., Uniformly factoring weakly compact operators, J. Funct. Anal. 266 (2014), no. 5, 2921–2943. https://doi.org/10.1016/j.jfa.2013.12.015

Beauzamy, B., Factorisation des propriétés de Banach-Saks, in “Séminaire sur la Géométrie des Espaces de Banach (1977--1978)'', Exp. No. 5, École Polytech., Palaiseau, 1978, pp. 1--16.

Brooker, P. A. H., Asplund operators and the Szlenk index, J. Operator Theory 68 (2012), no. 2, 405–442.

Causey, R. M., An alternate description of the Szlenk index with applications, Illinois J. Math. 59 (2015), no. 2, 359–390.

Causey, R. M., Proximity to $ell _p$ and $c_0$ in Banach spaces, J. Funct. Anal. 269 (2015), no. 12, 3952–4005. https://doi.org/10.1016/j.jfa.2015.10.001

Causey, R. M., A Ramsey theorem for trees with applications to weakly compact operators, Fund. Math. (to appear).

Davis, W. J., Figiel, T., Johnson, W. B., and Pełczyński, A., Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327.

Dodos, P., Banach spaces and descriptive set theory: selected topics, Lecture Notes in Mathematics, vol. 1993, Springer-Verlag, Berlin, 2010. https://doi.org/10.1007/978-3-642-12153-1

Dodos, P., Quotients of Banach spaces and surjectively universal spaces, Studia Math. 197 (2010), no. 2, 171–194. https://doi.org/10.4064/sm197-2-4

Dodos, P. and Ferenczi, V., Some strongly bounded classes of Banach spaces, Fund. Math. 193 (2007), no. 2, 171–179. https://doi.org/10.4064/fm193-2-5

Figiel, T., Factorization of compact operators and applications to the approximation problem, Studia Math. 45 (1973), 191–210. https://doi.org/10.4064/sm-45-2-191-210

Ghoussoub, N. and Maurey, B., $G_delta $-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), no. 1, 72–97. https://doi.org/10.1016/0022-1236(85)90039-4

Heinrich, S., Closed operator ideals and interpolation, J. Funct. Anal. 35 (1980), no. 3, 397–411. https://doi.org/10.1016/0022-1236(80)90089-0

James, R. C., A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc. 80 (1974), 738–743. https://doi.org/10.1090/S0002-9904-1974-13580-9

Johnson, W. B. and Szankowski, A., Complementably universal Banach spaces. II, J. Funct. Anal. 257 (2009), no. 11, 3395–3408. https://doi.org/10.1016/j.jfa.2009.07.008




How to Cite

Beanland, K., & Causey, R. M. (2018). Quantitative factorization of weakly compact, Rosenthal, and $\xi$-Banach-Saks operators. MATHEMATICA SCANDINAVICA, 123(2), 297–319. https://doi.org/10.7146/math.scand.a-105124