Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Summary:
We give an explicit description of a tensor norm equivalent on $C(K) \otimes F$ to the associated tensor norm $\nu _{qp}$ to the ideal of $(q,p)$-absolutely summing operators. As a consequence, we describe a tensor norm on the class of Banach spaces which is equivalent to the left projective tensor norm associated to $\nu _{qp}$.
References:
[1] A. Defant, K. Floret: Tensor norms and Operator Ideals. North-Holland Mathematics Studies 176. Amsterdam-London-New York-Tokyo, 1993. MR 1209438
[2] J. T. Lapresté: Operateurs sommantes et factorization à travers les espaces $L^p$. Studia Math. 56 (1976), 47–83. MR 0454704
[3] J. A. López Molina, E. A. Sánchez Pérez: Ideales de operadores absolutamente continuos. Rev. Real Acad. Ciencias Exactas, Fisicas y Naturales, Madrid 87 (1993), 349–378. MR 1318866
[4] U. Matter: Absolutely continuous operators and super-reflexivity. Math. Nachr. 130 (1987), 193–216. DOI 10.1002/mana.19871300118 | MR 0885628 | Zbl 0622.47045
[5] U. Matter, H. Jarchow: Interpolative constructions for operator ideals. Note di Matematica VIII (1988), no. 1, 45–56. MR 1050508
[6] B. Maurey: Sur certaines propriétés des opérateurs sommants. C. R. Acad. Sci. Paris A 277 (1973), 1053–1055. MR 0385621 | Zbl 0269.47014
[7] A. Pietsch: Operator Ideals. North-Holland Publ. Company, Amsterdam-New York-Oxford, 1980. MR 0582655 | Zbl 0455.47032
[8] G. Pisier: Factorization of operators through $L_{p,\infty }$ or $L_{p,1}$ and non-commutative generalizations. Math. Ann. 276 (1986), 105–136. DOI 10.1007/BF01450929 | MR 0863711
Search
Partner of
