On the volume of unit balls in Banach spaces

Carsten Schütt

Compositio Mathematica (1982)

  • Volume: 47, Issue: 3, page 393-407
  • ISSN: 0010-437X

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Schütt, Carsten. "On the volume of unit balls in Banach spaces." Compositio Mathematica 47.3 (1982): 393-407. <http://eudml.org/doc/89581>.

@article{Schütt1982,
author = {Schütt, Carsten},
journal = {Compositio Mathematica},
keywords = {pi-tensor product; volume ratio of symmetric spaces; unitary operator ideals; James space; Banach-Mazur distance},
language = {eng},
number = {3},
pages = {393-407},
publisher = {Martinus Nijhoff Publishers},
title = {On the volume of unit balls in Banach spaces},
url = {http://eudml.org/doc/89581},
volume = {47},
year = {1982},
}

TY - JOUR
AU - Schütt, Carsten
TI - On the volume of unit balls in Banach spaces
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 47
IS - 3
SP - 393
EP - 407
LA - eng
KW - pi-tensor product; volume ratio of symmetric spaces; unitary operator ideals; James space; Banach-Mazur distance
UR - http://eudml.org/doc/89581
ER -

References

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  1. [1] Y. Benyamini and Y. Gordon: Random factorisation of operators between Banach spaces. J. d'Anal. Math.39 (1981) 45-74. Zbl0474.47010MR632456
  2. [2] S. Chevet: Series de variables aleatoires Gaussiens a valeurs dans E ⊗ε F. Applications aux produit d'espaces de Wiener abstraits. Séminaire sur la geometrie des espaces de Banach (1977/8), expose XIX. Zbl0395.60004
  3. [3] G.H. Hardy and J.E. Littlewood: Bilinear forms bounded in spaces (p, q). Quart. J. Math. (Oxford) 5 (1934) 241-256. Zbl0010.36101JFM60.0335.01
  4. [4] R.I. Jamison and W.H. Ruckle: Factoring absolutely converging series. Math. Ann.224 (1976) 143-148. Zbl0319.40007MR435791
  5. [5] F. John: Extremum problems with inequalities as subsidiary conditions. R. Courant Anniversary Volume, InterscienceNew York, 1948, pp 187-204. Zbl0034.10503MR30135
  6. [6] W.B. Johnson and L. Tzafriri: Some more Banach spaces which do not have local unconditional structure. Houston J. Math.3 (1977) 55-60. Zbl0343.46014MR430753
  7. [7] G. Ja. Lozanovskii: On some Banach lattices I. Sibir. Mat. J.10, N° 3 (1969) 584-599, IIIibidem13, N° 6 (1972) 1304-1313 (Russian). Zbl0269.46008
  8. [8] A. Pelczyński and C. Schütt: Factoring the natural injection i (n): L∞n → L1n through finite dimensional Banach spaces and geometry of finite dimensional unitary ideals. Advances in Math., .Supplementary Studies, vol. 7B, 653-683. Zbl0484.46016
  9. [9] L.A. Santaló: Un invariante afin para los cuerpos convexos del espacio de n dimensiones. Port. Math.8 (1949) 155-161. Zbl0038.35702MR39293
  10. [10] C. Schütt: Unconditionality in tensor products. Israel J. Math.31 (1978) 209-216. Zbl0397.46017MR516148
  11. [11] S. Szarek and N. Tomczak-Jaegermann: On nearly Euclidean decomposition for some classes of Banach spaces. Composition Math.40 (1980) 367-385. Zbl0432.46018MR571056
  12. [12] Y. Gordon and S. Reisner: Some aspects of volume estimates to various parameters in Banach spaces Proc. Res. W. Banach sp. th., Univ. Iowa, 1981. Zbl0537.46024

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