• [1] R. G. Bartle, A general bilinear vector integral, Studia Math. 15 (1956), 337–352. MR 0080721 (18,289a)
• [2] R. G. Bartle, N. Dunford, and J. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289–305. MR 0070050 (16,1123c)
• [3] N. Bourbaki, Éléments de mathématique. XXV. Première partie. Livre VI: Intégration. Chapitre 6: Intégration vectorielle, Actualités Sci. Ind. No. 1281, Hermann, Paris, 1959 (French). MR 0124722 (23 #A2033)
• [4] Mahlon M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. Heft 21. Reihe: Reelle Funktionen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0094675 (20 #1187)
• [5] Nicolae Dinculeanu, Mesures vectorielles et opérations linéaires, C. R. Acad. Sci. Paris 246 (1958), 2328–2331 (French). MR 0096771 (20 #3254)
• [6] Nicolae Dinculeanu and Ciprian Foiaș, Mesures vectorielles et opérations linéaires sur 𝐿_{𝐸^{𝑝}}, C. R. Acad. Sci. Paris 248 (1959), 1759–1762 (French). MR 0105006 (21 #3753)
• [7] N. Dunford and J. Schwartz, Linear operators, Vol. I, Interscience, New York, 1958.
• [8] B. R. Gelbaum and J. Gil de Lamadrid, Bases of tensor products of Banach spaces, Pacific J. Math. 11 (1961), 1281–1286. MR 0147881 (26 #5394)
• [9] Jesús Gil de Lamadrid, On finite dimensional approximations of mappings in Banach spaces, Proc. Amer. Math. Soc. 13 (1962), 163–168. MR 0138972 (25 #2412), http://dx.doi.org/10.1090/S0002-9939-1962-0138972-1
• [10] Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 1955 (1955), no. 16, 140 (French). MR 0075539 (17,763c)
• [11] A. Grothendieck, La théorie de Fredholm, Bull. Soc. Math. France 84 (1956), 319–384 (French). MR 0088665 (19,558d)
• [12] Alexandra Ionescu Tulcea and Cassius Ionescu Tulcea, On the decomposition and integral representation of continuous linear operators, Ann. Mat. Pura Appl. (4) 53 (1961), 63–87. MR 0124728 (23 #A2039)
• [13] Alexandra Ionescu Tulcea and Cassius Ionescu Tulcea, On the lifting property. II. Representation of linear operators on spaces 𝐿_{𝐸^{𝑟}}, 1≤𝑟<∞, J. Math. Mech 11 (1962), 773–795. MR 0145350 (26 #2881)
• [14] R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc. 48 (1940), 516–541. MR 0004094 (2,318c), http://dx.doi.org/10.1090/S0002-9947-1940-0004094-3
• [15] Robert Schatten, A Theory of Cross-Spaces, Annals of Mathematics Studies, no. 26, Princeton University Press, Princeton, N. J., 1950. MR 0036935 (12,186e)
• [16] Juljusz Schauder, Eine Eigenschaft des Haarschen Orthogonalsystems, Math. Z. 28 (1928), no. 1, 317–320 (German). MR 1544958, http://dx.doi.org/10.1007/BF01181164
• [17] Ivan Zinger, Linear functionals on the space of continuous mappings of a compact Hausdorff space into a Banach space, Rev. Math. Pures Appl. 2 (1957), 301–315 (Russian). MR 0096964 (20 #3445)

Bibliography

[1]

R. G. Bartle, A general bilinear vector integral, Studia Math. 15 (1956), 337-352. MR 0080721 (18:289a)

[2]

R. G. Bartle, N. Dunford and J. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289-305. MR 0070050 (16:1123c)

[3]

N. Bourbaki, Eléments de mathématiques. VI. Intégrations, Actualités Sci. Ind. No. 1281, Hermann, Paris, 1952. MR 0124722 (23:A2033)

[4]

M. M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 21, Springer, Berlin, 1958. MR 0094675 (20:1187)

[5]

N. Dinculeanu, Mesures vectorielles et opérations linéaires, C. R. Acad. Sci. Paris 246 (1958), 2328-2331. MR 0096771 (20:3254)

[6]

N. Dinculeanu and C. Foias, Mesures vectorielles et opérations linéaires sur , C. R. Acad. Sci. Paris 248 (1959), 1759-1762. MR 0105006 (21:3753)

[7]

N. Dunford and J. Schwartz, Linear operators, Vol. I, Interscience, New York, 1958.

[8]

B. R. Gelbaum and J. Gil de Lamadrid, Bases of tensor products of Banach spaces, Pacific J. Math. 11 (1961), 1281-1286. MR 0147881 (26:5394)

[9]

J. Gil de Lamadrid, On finite dimensional approximations of mappings in Banach spaces, Proc. Amer. Math. Soc. 10 (1962), 163-168. MR 0138972 (25:2412)

[10]

A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955), 140 pp. MR 0075539 (17:763c)

[11]

-, La théorie de Fredholm, Bull. Soc. Math. France 84 (1956), 319-384. MR 0088665 (19:558d)

[12]

A. Ionescu Tulcea and C. Ionescu Tulcea, On the decomposition and integral representations of continuous linear operators, Ann. Mat. Pura Appl. 53 (1961), 81-88. MR 0124728 (23:A2039)

[13]

-, On the lifting property. II. Representation of linear operators on the spaces , J. Math. Mech. 7 (1962), 773-795. MR 0145350 (26:2881)

[14]

R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc. 48 (1938), 516-541. MR 0004094 (2:318c)

[15]

R. Schatten, A theory of cross-spaces, Annals of Mathematics Studies No. 26, Princeton Univ. Press, Princeton, N. J., 1950. MR 0036935 (12:186e)

[16]

J. Schauder, Eine Eigenschaft des Haarschen Orthogonal systems, Math. Z. 28 (1928), 317-320. MR 1544958

[17]

I. Singer, Linear functionals on spaces of continuous mappings of a compact Hausdorff space into a Banach space, Rev. Math. Pures Appl. 2 (1957), 309-315. (Russian) MR 0096964 (20:3445)