Evaluation maps, restriction maps, and compactness

 Access to full text

 Full (PDF)

1. [1] D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. 88 (1968), 35-46. Zbl0164.14903
2. [2] K. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241 (1979), 35-41. Zbl0398.46025
3. [3] R. G. Bartle, N. Dunford and J. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289-305. Zbl0068.09301
4. [4] E. M. Bator, Remarks on completely continuous operators, Bull. Polish Acad. Sci. Math. 37 (1987), 409-413. Zbl0767.46010
5. [5] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164. 
6. [6] R. G. Bilyeu and P. W. Lewis, Some mapping properties of representing measures, Ann. Mat. Pura Appl. 109 (1976), 273-287. Zbl0336.46048
7. [7] R. G. Bilyeu and P. W. Lewis, Vector measures and weakly compact operators on continuous function spaces: A survey, in: Measure Theory and its Applications, Proc. Measure Theory Conf., DeKalb, Ill., 1980, G. A. Goldin and R. F. Wheeler (eds.), Northern Illinois Univ., DeKalb, Ill, 1981, 165-172. 
8. [8] F. Bombal, On (V*) sets and Pełczyński's property (V*), Glasgow Math. J. 32 (1990), 109-120. 
9. [9] F. Bombal, On (V) and (V*) sets in vector-valued function spaces, preprint. Zbl0768.46025
10. [10] J. Bourgain and F. Delbaen, A class of special ${ℒ}_{\infty }$ spaces, Acta Math. 145 (1981), 155-176. Zbl0466.46024
11. [11] J. Bourgain and J. Diestel, Limited operators and strict cosingularity, Math. Nachr. 119 (1984), 55-58. Zbl0601.47019
12. [12] J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math. 92, Springer, 1984. 
13. [13] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977. 
14. [14] S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, New York, 1981. Zbl0484.46044
15. [15] N. Dunford and J. T. Schwartz, Linear Operators. I. General Theory, Pure and Appl. Math. 7, Interscience, New York, 1958. Zbl0084.10402
16. [16] J. Elton and E. Odell, The unit ball of every infinite-dimensional normed linear space contains a (1+ ε)-separated sequence, Colloq. Math. 44 (1981), 105-109. Zbl0493.46014
17. [17] G. Emmanuele, A dual characterization of Banach spaces not containing $l^1$, Bull. Polish Acad. Sci. Math. 34 (1986), 155-160. Zbl0625.46026
18. [18] G. Emmanuele, On the reciprocal Dunford-Pettis property in projective tensor products, Math. Proc. Cambridge Philos. Soc. 109 (1991), 161-166. Zbl0752.46042
19. [19] G. Emmanuele, Banach spaces on which Dunford-Pettis sets are relatively compact, Arch. Math. (Basel) 58 (1992), 477-485. Zbl0761.46010
20. [20] G. Emmanuele, personal communication. 
21. [21] A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129-173. Zbl0050.10902
22. [22] J. Hagler and W. B. Johnson, On Banach spaces whose dual balls are not weak* sequentially compact, Israel J. Math. 28 (1977), 325-330. Zbl0365.46019
23. [23] R. C. James, A non-reflexive Banach space isometric with its second conjugate, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 174-177. Zbl0042.36102
24. [24] R. C. James, Separable conjugate spaces, Pacific J. Math. 10 (1960), 563-571. Zbl0096.31301
25. [25] T. Leavelle, The reciprocal Dunford-Pettis and Radon-Nikodym properties in Banach spaces, Ph.D. dissertation, Univ. of North Texas, 1984. 
26. [26] E. Odell and H. P. Rosenthal, A double-dual characterization of separable Banach spaces containing $l^1$, Israel J. Math. 20 (1975), 375-384. Zbl0312.46031
27. [27] A. Pełczyński, Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 641-648. Zbl0107.32504
28. [28] A. Pełczyński, On strictly singular and stictly cosingular operators. II, ibid. 13 (1965), 37-41. Zbl0138.38604
29. [29] H. Rosenthal, A characterization of Banach spaces containing $l^1$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411-2413. Zbl0297.46013
30. [30] H. Rosenthal, Pointwise compact subsets of the first Baire class, Amer. J. Math. 99 (1977), 362-378. Zbl0392.54009
31. [31] E. Saab, Some characterizations of weak Radon-Nikodym sets, Proc. Amer. Math. Soc. 86 (1982), 307-311. Zbl0494.46047
32. [32] I. Singer, Bases in Banach Spaces II, Springer, 1981. Zbl0467.46020

1. Mahdi Dehghani, Mohammad B. Dehghani, Mohammad S. Moshtaghioun, Sequentially Right Banach spaces of order $p$
2. Ioana Ghenciu, Property $\left(\mathrm{𝐰𝐋}\right)$ and the reciprocal Dunford-Pettis property in projective tensor products