On integration in banach spaces and total sets

References

• K.T. Andrews, Universal Pettis integrability, Canad. J. Math. 37(1) (1985), 141–159. doi: 10.4153/CJM-1985-011-5
   Web of Science ®Google Scholar
• G. Androulakis and M. Ziemke, The closedness of the generator of a semigroup, Semigroup Forum 93(3) (2016), 589–606. doi: 10.1007/s00233-015-9738-9
   Web of Science ®Google Scholar
• A. Avilés, G. Martínez-Cervantes, and J. Rodríguez, Weak∗-sequential properties of Johnson-Lindenstrauss spaces, J. Funct. Anal., (2018), https://doi.org/10.1016/j.jfa.2018.09.007
   Web of Science ®Google Scholar
• J. Bonet and B. Cascales, Noncomplete Mackey topologies on Banach spaces, Bull. Aust. Math. Soc. 81(3) (2010), 409–413. doi: 10.1017/S0004972709001154
   Web of Science ®Google Scholar
• J. Bourgain and H.P. Rosenthal, Applications of the theory of semi-embeddings to Banach space theory, J. Funct. Anal. 52(2) (1983), 149–188. doi: 10.1016/0022-1236(83)90080-0
   Web of Science ®Google Scholar
• R.D. Bourgin, Geometric aspects of convex sets with the Radon-Nikodým property, Lecture Notes in Mathematics, Vol. 993, Springer-Verlag, Berlin, 1983. doi: 10.1007/BFb0069321
   Google Scholar
• B. Cascales, V. Kadets, and J. Rodríguez, Radon-Nikodým theorems for multimeasures in non-separable spaces, Zh. Mat. Fiz. Anal. Geom. 9(1) (2013), 7–24.
   Web of Science ®Google Scholar
• B. Cascales and J. Rodríguez, Birkhoff integral for multi-valued functions, J. Math. Anal. Appl. 297(2) (2004), 540–560. doi: 10.1016/j.jmaa.2004.03.026
   Web of Science ®Google Scholar
• R. Deville and G. Godefroy, Some applications of projective resolutions of identity, Proc. London Math. Soc. (3) 67(1) (1993), 183–199. doi: 10.1112/plms/s3-67.1.183
   Google Scholar
• R. Deville and J. Rodríguez, Integration in Hilbert generated Banach spaces, Israel J. Math. 177 (2010), 285–306. doi: 10.1007/s11856-010-0047-4
   Web of Science ®Google Scholar
• J. Diestel and B. Faires, On vector measures, Trans. Amer. Math. Soc. 198 (1974), 253–271. doi: 10.1090/S0002-9947-1974-0350420-8
   Web of Science ®Google Scholar
• J. Diestel and J.J. Uhl, Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977.
   Google Scholar
• J. Diestel and J.J. Uhl, Progress in vector measures—1977–83, Measure theory and its applications (Sherbrooke, Que., 1982), Lecture Notes in Math., Vol. 1033, pp. 144–192, Springer, Berlin, 1983.
   Google Scholar
• G.A. Edgar, Measurability in a Banach space, Indiana Univ. Math. J. 26(4) (1977), 663–677. doi: 10.1512/iumj.1977.26.26053
   Web of Science ®Google Scholar
• G.A. Edgar, Measurability in a Banach space, II, Indiana Univ. Math. J. 28(4) (1979), 559–579. doi: 10.1512/iumj.1979.28.28039
   Web of Science ®Google Scholar
• G.A. Edgar, An ordering for the Banach spaces, Pacific J. Math. 108(1) (1983), 83–98. doi: 10.2140/pjm.1983.108.83
   Web of Science ®Google Scholar
• J. Ferrer, P. Koszmider, and W. Kubiś, Almost disjoint families of countable sets and separable complementation properties, J. Math. Anal. Appl. 401(2) (2013), 939–949. doi: 10.1016/j.jmaa.2013.01.008
   Web of Science ®Google Scholar
• N. Ghoussoub and E. Saab, On the weak Radon-Nikodým property, Proc. Amer. Math. Soc. 81(1) (1981), 81–84.
   Web of Science ®Google Scholar
• A.J. Guirao, G. Martínez-Cervantes, and J. Rodríguez, Completeness in the Mackey topology by norming subspaces, preprint, (arXiv: 1812.10669).
   Google Scholar
• A.J. Guirao and V. Montesinos, Completeness in the Mackey topology, Funct. Anal. Appl. (2) 49 (2015), 97–105. doi: 10.1007/s10688-015-0091-2
   Google Scholar
• A.J. Guirao, V. Montesinos, and V. Zizler, A note on Mackey topologies on Banach spaces, J. Math. Anal. Appl. 445(1) (2017), 944–952. doi: 10.1016/j.jmaa.2016.08.030
   Web of Science ®Google Scholar
• A.B. Gulisashvili, Estimates for the Pettis integral in interpolation spaces, and a generalization of some imbedding theorems, Soviet Math., Dokl. 25 (1982), 428–432.
   Google Scholar
• P. Hájek, V. Montesinos Santalucía, J. Vanderwerff, and V. Zizler, Biorthogonal systems in Banach spaces, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, Vol. 26, Springer, New York, 2008.
   Google Scholar
• G. Köthe, Topological vector spaces, I, Die Grundlehren der mathematischen Wissenschaften, Band 159, Springer-Verlag New York Inc., New York, 1969.
   Google Scholar
• M. Kunze, A Pettis-type integral and applications to transition semigroups, Czechoslovak Math. J. 61(136)(2) (2011), 437–459. doi: 10.1007/s10587-011-0065-3
   Google Scholar
• J. Kupka, Radon-Nikodym theorems for vector valued measures, Trans. Amer. Math. Soc. 169 (1972), 197–217. doi: 10.1090/S0002-9947-1972-0311871-9
   Web of Science ®Google Scholar
• G. Martínez-Cervantes, Banach spaces with weak*-sequential dual ball, Proc. Amer. Math. Soc. 146(4) (2018), 1825–1832. doi: 10.1090/proc/13843
   Web of Science ®Google Scholar
• K. Musia-l, The weak Radon-Nikodým property in Banach spaces, Studia Math. 64(2) (1979), 151–173. doi: 10.4064/sm-64-2-151-174
   Web of Science ®Google Scholar
• K. Musia-l, Topics in the theory of Pettis integration, Rend. Istit. Mat. Univ. Trieste 23(1) (1993), 177–262.
   Google Scholar
• R. Neidinger and H.P. Rosenthal, Norm-attainment of linear functionals on sub- spaces and characterizations of Tauberian operators, Pacific J. Math. 118(1) (1985), 215–228. doi: 10.2140/pjm.1985.118.215
   Web of Science ®Google Scholar
• J. Orihuela, On weakly Lindelöf Banach spaces, Progress in functional analysis (Peñíscola, 1990), North-Holland Math. Stud., Vol. 170, pp. 279–291, North-Holland, Amsterdam, 1992.
   Google Scholar
• A. Plichko, Three sequential properties of dual Banach spaces in the weak∗ topology, Topology Appl. 190 (2015), 93–98. doi: 10.1016/j.topol.2015.04.017
   Web of Science ®Google Scholar
• R. Pol, A function space C(X) which is weakly Lindelöf but not weakly compactly generated, Studia Math. 64(3) (1979), 279–285. doi: 10.4064/sm-64-3-279-285
   Web of Science ®Google Scholar
• J. Rodríguez and G. Vera, Uniqueness of measure extensions in Banach spaces, Studia Math. 175(2) (2006), 139–155. doi: 10.4064/sm175-2-3
   Web of Science ®Google Scholar
• J. Vanderwerff, J.H.M. Whitfield, and V. Zizler, Markuševič bases and Corson compacta in duality, Canad. J. Math. 46(1) (1994), 200–211. doi: 10.4153/CJM-1994-007-5
   Web of Science ®Google Scholar
• D. van Dulst, Characterizations of Banach spaces not containing l1, CWI Tract, Vol. 59, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.
   Google Scholar