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Lower bounds for normal structure coefficients. (English) Zbl 0787.46010

The authors give lower bounds for the weakly convergent sequences coefficient \(\text{WCS}(X)\) of a Banach space \(X\) by using the modulus of uniform convexity and the modules of nearly uniform convexity, respectively. The first estimate improves the existing ones, while the second is exact for \(\ell^ p\)-spaces.

MSC:

46B20 Geometry and structure of normed linear spaces
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[1] DOI: 10.4153/CMB-1987-027-8 · Zbl 0585.46011 · doi:10.4153/CMB-1987-027-8
[2] Bynum, Pacific J. Math. 86 pp 427– (1980) · Zbl 0442.46018 · doi:10.2140/pjm.1980.86.427
[3] Amir, Pacific J. Math. 118 pp 1– (1985) · Zbl 0529.46011 · doi:10.2140/pjm.1985.118.1
[4] Akhmerov, Measures of noncompactness and condensing operators (1986)
[5] Prus, Atti. Sem. Mat. Fis. Univ. Modena 38 pp 535– (1990)
[6] DOI: 10.1090/S0002-9939-1983-0695255-2 · doi:10.1090/S0002-9939-1983-0695255-2
[7] Lim, Pacific J. Math. 111 pp 357– (1984) · Zbl 0495.46012 · doi:10.2140/pjm.1984.111.357
[8] DOI: 10.2307/2313345 · Zbl 0141.32402 · doi:10.2307/2313345
[9] DOI: 10.1216/RMJ-1980-10-4-743 · Zbl 0505.46011 · doi:10.1216/RMJ-1980-10-4-743
[10] Benavides, Proc. Roy. Soc. Edinburgh Sect. A 117 pp 299– (1991) · Zbl 0742.46012 · doi:10.1017/S0308210500024744
[11] Goebel, Ann. Univ. Marie-Curie Sklodowska Sect. A 38 pp 41– (1984)
[12] DOI: 10.1112/jlms/s2-34.1.120 · Zbl 0578.47045 · doi:10.1112/jlms/s2-34.1.120
[13] DOI: 10.1016/0022-247X(88)90121-7 · Zbl 0679.47028 · doi:10.1016/0022-247X(88)90121-7
[14] DOI: 10.1016/0362-546X(85)90055-0 · Zbl 0526.47034 · doi:10.1016/0362-546X(85)90055-0
[15] Arias, Proc. Amer. Math. Soc. 112 pp 1087– (1991)
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