International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 653-658

p-representable operators in Banach spaces

Roshdi Khalil

Department of Mathematics, The University of Michigan, Ann Arbor 48109, Michigan, USA

Received 7 November 1985

Copyright © 1986 Roshdi Khalil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let E and F be Banach spaces. An operator TL(E,F) is called p-representable if there exists a finite measure μ on the unit ball, B(E*), of E* and a function gLq(μ,F), 1p+1q=1, such thatTx=B(E*)x,x*g(x*)dμ(x*)for all xE. The object of this paper is to investigate the class of all p-representable operators. In particular, it is shown that p-representable operators form a Banach ideal which is stable under injective tensor product. A characterization via factorization through Lp-spaces is given.