Abstract :
In this paper we use results from the theory of tensor products of Banach spaces to establish the
isometry of the space of (1,p)-summing sequences (also known as strongly p-summable sequences)
in a Banach space X, the space of nuclear X-valued operators on p and the complete projective
tensor product of p with X. Through similar techniques from the theory of tensor products,
the isometry of the sequence space Lp X (recently introduced in a paper by Bu, Quaestiones
Math. (2002), to appear), the space of nuclear X-valued operators on Lp(0, 1) (with a suitable
equivalent norm) and the complete projective tensor product of Lp(0, 1) with X is established.
Moreover, we find conditions for the space of (p, q)-summing multipliers to have the GAK-property
(generalized AK-property), use multiplier sequences to characterize Banach space valued bounded
linear operators on the vector sequence space of absolutely p-summable sequences in a Banach space
and present short proofs for results on p-summing multipliers.
2003 Elsevier Science (USA). All rights reserved.
