Evaluation maps, restriction maps, and compactness
Bator, Elizabeth ; Lewis, Paul ; Ochoa, James
Colloquium Mathematicae, Tome 78 (1998), p. 1-17 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:210601 
@article{bwmeta1.element.bwnjournal-article-cmv78z1p1bwm,
     author = {Elizabeth Bator and Paul Lewis and James Ochoa},
     title = {Evaluation maps, restriction maps, and compactness},
     journal = {Colloquium Mathematicae},
     volume = {78},
     year = {1998},
     pages = {1-17},
     zbl = {0948.46008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv78z1p1bwm}
}

Bator, Elizabeth; Lewis, Paul; Ochoa, James. Evaluation maps, restriction maps, and compactness. Colloquium Mathematicae, Tome 78 (1998) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv78z1p1bwm/

[000] [1] D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. 88 (1968), 35-46. | Zbl 0164.14903

[001] [2] K. Andrews, Dunford-Pettis sets in the space of Bochner integrable functions, Math. Ann. 241 (1979), 35-41. | Zbl 0398.46025

[002] [3] R. G. Bartle, N. Dunford and J. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289-305. | Zbl 0068.09301

[003] [4] E. M. Bator, Remarks on completely continuous operators, Bull. Polish Acad. Sci. Math. 37 (1987), 409-413. | Zbl 0767.46010

[004] [5] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164.

[005] [6] R. G. Bilyeu and P. W. Lewis, Some mapping properties of representing measures, Ann. Mat. Pura Appl. 109 (1976), 273-287. | Zbl 0336.46048

[006] [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.

[007] [8] F. Bombal, On (V*) sets and Pełczyński's property (V*), Glasgow Math. J. 32 (1990), 109-120.

[008] [9] F. Bombal, On (V) and (V*) sets in vector-valued function spaces, preprint. | Zbl 0768.46025

[009] [10] J. Bourgain and F. Delbaen, A class of special ℒ∞ spaces, Acta Math. 145 (1981), 155-176. | Zbl 0466.46024

[010] [11] J. Bourgain and J. Diestel, Limited operators and strict cosingularity, Math. Nachr. 119 (1984), 55-58. | Zbl 0601.47019

[011] [12] J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math. 92, Springer, 1984.

[012] [13] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.

[013] [14] S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, New York, 1981. | Zbl 0484.46044

[014] [15] N. Dunford and J. T. Schwartz, Linear Operators. I. General Theory, Pure and Appl. Math. 7, Interscience, New York, 1958. | Zbl 0084.10402

[015] [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. | Zbl 0493.46014

[016] [17] G. Emmanuele, A dual characterization of Banach spaces not containing l1, Bull. Polish Acad. Sci. Math. 34 (1986), 155-160. | Zbl 0625.46026

[017] [18] G. Emmanuele, On the reciprocal Dunford-Pettis property in projective tensor products, Math. Proc. Cambridge Philos. Soc. 109 (1991), 161-166. | Zbl 0752.46042

[018] [19] G. Emmanuele, Banach spaces on which Dunford-Pettis sets are relatively compact, Arch. Math. (Basel) 58 (1992), 477-485. | Zbl 0761.46010

[019] [20] G. Emmanuele, personal communication.

[020] [21] A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129-173. | Zbl 0050.10902

[021] [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. | Zbl 0365.46019

[022] [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. | Zbl 0042.36102

[023] [24] R. C. James, Separable conjugate spaces, Pacific J. Math. 10 (1960), 563-571. | Zbl 0096.31301

[024] [25] T. Leavelle, The reciprocal Dunford-Pettis and Radon-Nikodym properties in Banach spaces, Ph.D. dissertation, Univ. of North Texas, 1984.

[025] [26] E. Odell and H. P. Rosenthal, A double-dual characterization of separable Banach spaces containing l1, Israel J. Math. 20 (1975), 375-384. | Zbl 0312.46031

[026] [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. | Zbl 0107.32504

[027] [28] A. Pełczyński, On strictly singular and stictly cosingular operators. II, ibid. 13 (1965), 37-41. | Zbl 0138.38604

[028] [29] H. Rosenthal, A characterization of Banach spaces containing l1, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411-2413. | Zbl 0297.46013

[029] [30] H. Rosenthal, Pointwise compact subsets of the first Baire class, Amer. J. Math. 99 (1977), 362-378. | Zbl 0392.54009

[030] [31] E. Saab, Some characterizations of weak Radon-Nikodym sets, Proc. Amer. Math. Soc. 86 (1982), 307-311. | Zbl 0494.46047

[031] [32] I. Singer, Bases in Banach Spaces II, Springer, 1981. | Zbl 0467.46020