Some applications of Q-points and Lebesgue filters to Banach spaces
DOI:
https://doi.org/10.17398/Palabras clave:
Q-point, Katětov order, L-sequence, L-elementResumen
We present a new characterization of Q-point ultrafilters and use it to optimize the result of Avilés, Martı́nez-Cervantes, and Rueda Zoca linking the existence of L-orthogonal sequences and L-orthogonal elements in Banach spaces via ultrafilter limits.
Descargas
Referencias
A. Avilés, G. Martı́nez-Cervantes, A. Rueda Zoca, Banach spaces containing c0 and elements in the fourth dual, J. Math. Anal. Appl. 508 (2) (2022), Paper No. 125911, 10 pp.
A. Avilés, G. Martı́nez-Cervantes, A. Rueda Zoca, L-orthogonal elements and L-orthogonal sequences, Int. Math. Res. Not. IMRN (2023), n. 11, 9128 – 9154.
D.H. Fremlin, Measure-centering ultrafilters, in “Ultrafilters across mathematics”, Contemp. Math., 530, Amer. Math. Soc., Providence, RI, 2010, 73 – 120.
G. Godefroy, Metric characterization of first Baire class linear forms and octahedral norms, Studia Math. 95 (1) (1989), 1 – 15.
M. Hrušák, Combinatorics of filters and ideals, in “Set theory and its applications”, Contemp. Math., 533, Amer. Math. Soc., Providence, RI, 2011, 26 – 69, DOI: 10.1090/conm/533/10503.
M. Hrušák, Katětov order on Borel ideals, Arch. Math. Logic 56 (2017), 831 – 847.
M. Hrušák, D. Meza-Alcántara, Katětov order, Fubini property and Hausdorff ultrafilters, Rend. Istit. Mat. Univ. Trieste 44 (2012), 503 – 511.
M. Hrušák, D. Meza-Alcántara, H. Minami, Pair-splitting, pair-reaping and cardinal invariants of Fσ -ideals, J. Symbolic Logic 75 (2) (2010), 661 – 677.
V. Kadets, A. Leonov, Dominated convergence and Egorov theorems for filter convergence, J. Math. Phys. Anal. Geom. 3 (2007), 196 – 212.
V. Kadets, V. Shepelska, D. Werner, Thickness of the unit sphere, `1 -types, and the almost Daugavet property, Houston J. Math. 37 (2011), 867 – 878.
V. Kanovei, M. Reeken, New Radon-Nikodym ideals, Mathematika 47 (1-2) (2000), 219 – 227.
A.R.D. Mathias, Happy families, Ann. Math. Logic 12 (1) (1977), 59 – 111.
H.L. Royden, “Real analysis”, 2d ed., Macmillan Publishing Company, New York, 1968.
S. Solecki, Filters and sequences, Fund. Math. 163 (3) (2000), 215 – 228.
Descargas
Publicado
Número
Sección
Licencia
Derechos de autor 2024 The authors
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.
