Asymptotic estimates for approximation quantities of tensor product identities

Journal of Approximation Theory

Volumn 88, Issue 2, 1997, Pages 228-256

  Carl, Bernd ^a   Defant, Andreas ^b  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b UNIVERSITY OF OLDENBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031068925     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1996.2995     Document Type: Article

References (22)

1. [BG] Y. Benjamini and Y. Gordon, Random factorization of operators between Banach spaces, J. Anal. Math. 39 (1981), 45-74.
2. p-spaces, Trans. Amer. Math. Soc. 391 (1992), 55-76.
3. [CS] B. Carl and I. Stephani, "Entropy, Compactness and the Approximation of Operators," Cambridge University Tracts in Mathematics, Vol. 98, Cambridge Univ. Press, Cambridge, 1990.
4. [DF] A. Defant and K. Floret, "Tensor Norms and Operator Ideals," North Holland Math. Studies, Vol. 176, North-Holland, Amsterdam, 1993.
5. [ET] D. E. Edmunds and H. S. Tylli, Entropy estimates of tensor products of operators, Ark. Mat. 31 (1993), 247-274.
6. ∞ and estimates of the Gordon-Lewis constant, Israel J. Math. 37 (1980), 92-111.
7. [GG] A. Garnaev and E. Gluskin, On diameters of the Euclidean sphere, Dokl. A.N.U.S.S.R. 277 (1984), 1048-1052.
8. [GKS] Y. Gordon, H. König, and C. Schütt, Geometric and probabilistc estimates for entropy and approximation numbers of operators, J. Approx. Theory 49 (1987), 219-239.
9. [GL] Y. Gordon and D. R. Lewis, Absolutely summing operators and local unconditional structure, Acta Math. 133 (1974), 27-48.
10. [HL] G. H. Hardy and J. E. Littlewood, Bilinear forms bounded in space (p, q), Quart. J. Math. Oxford Ser. 5 (1934), 241-254.
11. [H] S. Heinrich, Complexity of integral equations and relations to s-numbers, J. Complexity, to appear.
12. [I] R. S. Ismagilov, Diameters of sets in normed linear spaces and the approximation of functions by trigonometric polynomials, Russian Math. Surveys 29 (1974), 169-186.
13. [K] Her. König, "Eigenvalue Distribution of Compact Operators," Birkhäuser, Basel, 1986.
14. [L] D. R. Lewis, An isomorphic characterization of the Schmidt class, Compositio Math. Ann. 201 (1973), 201-209.
15. [PT] A. Pajor and N. Tomczak-Jaegermann, Subspaces of small codimension of finite dimensional Banach spaces, Proc. Amer. Math. Soc. 97 (1986), 637-642.
16. [P1] A. Pietsch, "Operator Ideals," Deutscher Verlag der Wiss., 1978; North-Holland, Amsterdam, 1980.
17. [P2] A. Pietsch, "Eigenvalues and s-Numbers," Akad. Verlagsges., 1987; Cambridge Studies in Advanced Mathematics, Vol. 13, Cambridge, 1987.
18. [P] G. Pisier, "Volume of Convex Bodies and Banach Space Geometry," Cambridge University Tracts in Mathematics, Vol. 94, Cambridge, 1989.
19. [Pi] A. Pinkus, "n-Widths in Approximation Theory," Springer-Verlag, Berlin/New York, 1985.
20. [S1] C. Schütt, On the Banach-Mazur distance of finite-dimensional symmetric Banach spaces and the hypergeometric distribution, Studia Math. 72 (1982), 109-129.
21. [S2] C. Schütt, On the volume of unit balls in Banach spaces, Composito Math. 47 (1982), 393-407.
22. [T] N. Tomczak-Jaegermann, "Banach-Mazur Distances and Finite Dimensional Operator Ideals," Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 38, Longman Sci. Tech., Harlow, 1989.