A theorem of Giesy and James states that c0 is nitely representable in James' quasire exive Banach space J2. We extend this theorem to the p th quasi-re exive James space Jp for each p ∈ (1,∞). As an application, we obtain a new closed ideal of operators on Jp, namely the closure of the set of operators that factor through the complemented subspace (`∞ ⊕ `∞ ⊕ · · · ⊕ `∞ ⊕ · · · )`p of Jp. 2010 ...

1991 Mathematics Subject Classi cation: 11Y40

1991 Mathematics Subject Classi cation: Primary 60K35.

1991 Mathematics Subject Classi cation: 11F11, 11E20.

1991 Mathematics Subject Classi cation. Primary: 11F75. Secondary: 11F67, 12F12.

1991 Mathematics Subject Classi cation. Primary: 11D25; Secondary: 11G05, 11Y50

1991 Mathematics Subject Classi cation: Primary 11R06, 11K16; Secondary 11Y99.

1991 Mathematics Subject Classi cation. Primary: 11F75. Secondary: 11F67, 12F12.

Research supported by NSA and NSF. 1980 Mathematics Subject Classi cation (1985 Revision): 20E99.

Mathematics Subject Classi cation: Primary, 11R20, 11R29, 11Y40; Secondary, 11M20, 11R42.