dc.contributor.author | Montgomery-Smith, Stephen, 1963- | eng |
dc.contributor.author | Saab, Paulette, 1952- | eng |
dc.date.issued | 2011 | eng |
dc.description | The final version of this paper appears in: "Proceedings of the Royal Society of Edinburgh, Section B" 120A (1992): 283-296. Print. | eng |
dc.description.abstract | Let X, Y and Z be Banach spaces, and let Πp(Y,Z) (1 ≤ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a £∞-space, then a bounded linear operator T:X⊗εY→Z is 1-summing if and only if a naturally associated operator T#:X→Π1(Y,Z) is 1-summing. This result need not be true if X is not a £∞-space. For p > 1, several examples are given with X = C[0,1] to show that T# can be p-summing without T being p-summing. Indeed, there is an operator T on C[0,1]⊗εl1 whose associated operator T# is 2-summing, but for all N∈N, there exists an N-dimensional subspace U of C[0,1]⊗εl1 such that T restricted to U is equivalent to the identity operator on l∞N. Finally, we show that there is a compact Hausdorff space K and a bounded linear operator T:C(K)⊗εl1→l2 for which T#:C(K)→Π1(l1,l2) is not 2-summing. | eng |
dc.identifier.uri | http://hdl.handle.net/10355/9838 | eng |
dc.language | English | eng |
dc.relation.ispartof | Mathematics publications (MU) | eng |
dc.relation.ispartofcommunity | University of Missouri-Columbia. College of Arts and Sciences. Department of Mathematics | eng |
dc.rights | OpenAccess. | eng |
dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. | |
dc.subject | Integral norm | eng |
dc.subject.lcsh | Integral operators | eng |
dc.subject.lcsh | Hilbert space | eng |
dc.title | p-summing operators on injective tensor products of spaces | eng |
dc.type | Preprint | eng |