S. Kakutani

Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Annals of Mathematics (2) 42 (1941), pp. 523-537.

Concrete representation of abstract (M)-spaces (A characterization of the space of continuous functions), Annals of Mathematics (2) 42 (1941), pp. 994-1024.

F. Cunningham, Jr.

L-structure in L-spaces, Transactions A.M.S. 95 (1960), pp. 274-299.

M-structure in Banach spaces, Proc. Cambridge Philos. Soc. 63 (1967), pp. 613-629.

E. Behrends
L^p-Struktur in Banachräumen, Studia Math. 55 (1976), pp. 71-85.

L^p-Struktur in Banachräumen, II, Studia Math. 62 (??).

From Theorem 1.3, p. 8, of Springer LNM # 613 (1977), L^p-Structure in Real Banach Spaces:

The space (R², || ||₁) (≈ (R², || ||_∞)) is the only [real] Banach space which admits non-trivial L^p-projections for two different values of p [and that only for p=1, p=∞ ].

Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Annals of Mathematics (2) 42 (1941), pp. 523-537.

Concrete representation of abstract (M)-spaces (A characterization of the space of continuous functions), Annals of Mathematics (2) 42 (1941), pp. 994-1024.

L-structure in L-spaces, Transactions A.M.S. 95 (1960), pp. 274-299.

M-structure in Banach spaces, Proc. Cambridge Philos. Soc. 63 (1967), pp. 613-629.

From Theorem 1.3, p. 8, of Springer LNM # 613 (1977), L^p-Structure in Real Banach Spaces:

The space (R², || ||₁) (≈ (R², || ||_∞)) is the only [real] Banach space which admits non-trivial L^p-projections for two different values of p [and that only for p=1, p=∞ ].

Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Annals of Mathematics (2) 42 (1941), pp. 523-537.

Concrete representation of abstract (M)-spaces (A characterization of the space of continuous functions), Annals of Mathematics (2) 42 (1941), pp. 994-1024.

L-structure in L-spaces, Transactions A.M.S. 95 (1960), pp. 274-299.

M-structure in Banach spaces, Proc. Cambridge Philos. Soc. 63 (1967), pp. 613-629.

From Theorem 1.3, p. 8, of Springer LNM # 613 (1977), Lp-Structure in Real Banach Spaces:

The space (R2, || ||1) (≈ (R2, || ||∞)) is the only [real] Banach space which admits non-trivial Lp-projections for two different values of p [and that only for p=1, p=∞ ].

From Theorem 1.3, p. 8, of Springer LNM # 613 (1977), L^p-Structure in Real Banach Spaces:

The space (R², || ||₁) (≈ (R², || ||_∞)) is the only [real] Banach space which admits non-trivial L^p-projections for two different values of p [and that only for p=1, p=∞ ].