Inclusions and coincidences for multiple Cohen positive strongly \(p\)-summing \(m\)-linear operators. (English) Zbl 1538.47006
Summary: We compare a new class of multiple Cohen positive strongly \(p\)-summing multilinear operators along with different classes of positive multilinear \(p\)-summability and investigate a duality relationship in terms of the tensor norm.
MSC:
| 47A07 | Forms (bilinear, sesquilinear, multilinear) |
| 46A20 | Duality theory for topological vector spaces |
| 46B42 | Banach lattices |
| 47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |
| 47B65 | Positive linear operators and order-bounded operators |
Keywords:
Banach lattice; multiple Cohen strongly summing operators; positive \(p\)-summing operators; positive strongly \(p\)-summing operators; tensor normReferences:
| [1] | D. Achour and A. Belacel, Domination and factorization theorems for positive strongly p-summing operators, Positivity 18 (2014), no. 4, 785-804. · Zbl 1328.47020 |
| [2] | O. Blasco, Positive p-summing operators on L p -spaces. Proc. Amer. Math. Soc. 100 (1987), no. 2, 275-280. · Zbl 0622.47013 |
| [3] | A. Bougoutaia and A. Belacel. Cohen positive strongly p-summing and p-convex multilinear operators, Positivity 23 (2019), no. 2, 379-395. · Zbl 1447.46032 |
| [4] | A. Bougoutaia, A. Belacel, and H. Hamdi, Domination and Kwapień’s factorization theo-rems for positive Cohen nuclear linear operators, Moroccan J. Pure Appl. Anal. 7 (2021), no. 1, 100-115. · Zbl 07836878 |
| [5] | Q. Bu and C.C.A. Labuschagne, Positive multiple summing and concave multilinear oper-ators on Banach lattices, Mediterr. J. Math. 12 (2015), no. 1, 77-87. · Zbl 1331.46038 |
| [6] | J.R. Campos, Cohen and multiple Cohen strongly summing multilinear operators, Linear Multilinear Algebra 62 (2014), no. 3, 322-346. · Zbl 1315.47078 |
| [7] | J.S. Cohen, Absolutely p-summing, p-nuclear operators and their conjugates, Math. Ann. 201 (1973) 177-200. · Zbl 0233.47019 |
| [8] | J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators. Cambridge Studies in Advanced Mathematics, 43. Cambridge University Press, Cambridge, 1995. · Zbl 0855.47016 |
| [9] | M.C. Matos, Fully absolutely summing and Hilbert-Schmidt multilinear mappings, Collect. Math. 54 (2003), no. 2, 111-136. · Zbl 1078.46031 |
| [10] | Y. Meléndez and A. Tonge, Polynomials and the Pietsch domination theorem, Math. Proc. R. Ir. Acad. 99A (1999), no. 2, 195-212. · Zbl 0973.46037 |
| [11] | D. Pellegrino and J. Santos, Absolutely summing multilinear operators: a panorama, Quaest. Math. 34 (2011), no. 4, 447-478. · Zbl 1274.47001 |
| [12] | D. Pérez-García and I. Villanueva, Multiple summing operators on C(K) spaces. Ark. Mat. 42 (2004), no. 1, 153-171. · Zbl 1063.46032 |
| [13] | D. Popa. Multiple summing, dominated and summing operators on a product of l 1 spaces, Positivity 18 (2014), no. 4, 751-765. · Zbl 1321.46048 |
| [14] | R.A. Ryan. Introduction to Tensor Products of Banach Spaces, Springer-Verlag London Ltd. London, 2002. · Zbl 1090.46001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
