• [1] Leon Alaoglu, Weak topologies of normed linear spaces, Ann. of Math. (2) 41 (1940), 252–267. MR 0001455 (1,241e)
• [2] P. Alexandroff and H. Hopf, Topologie I, Berlin, 1935.
• [3] S. Banach, Théorie des Opérations Linéares, Warsaw, 1932.
• [4] Garrett Birkhoff, Integration of functions with values in a Banach space, Trans. Amer. Math. Soc. 38 (1935), no. 2, 357–378. MR 1501815, http://dx.doi.org/10.1090/S0002-9947-1935-1501815-3
• [5] Garrett Birkhoff, Moore-Smith convergence in general topology, Ann. of Math. (2) 38 (1937), no. 1, 39–56. MR 1503323, http://dx.doi.org/10.2307/1968508
• [6] S. Bochner, Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind, Fundamenta Mathematicae, vol. 20 (1933), pp. 262-276.
• [7] S. Bochner and A. E. Taylor, Linear functionals on certain spaces of abstractly-valued functions, Ann. of Math. (2) 39 (1938), no. 4, 913–944. MR 1503445, http://dx.doi.org/10.2307/1968472
• [8] Mahlon M. Day, Regularity of function-to-function transformations, Bull. Amer. Math. Soc. 45 (1939), no. 4, 296–303. MR 1563970, http://dx.doi.org/10.1090/S0002-9904-1939-06966-8
• [9] Mahlon M. Day, Reflexive Banach spaces not isomorphic to uniformly convex spaces, Bull. Amer. Math. Soc. 47 (1941), 313–317. MR 0003446 (2,221b), http://dx.doi.org/10.1090/S0002-9904-1941-07451-3
• [10] Nelson Dunford, Integration in general analysis, Trans. Amer. Math. Soc. 37 (1935), no. 3, 441–453. MR 1501796, http://dx.doi.org/10.1090/S0002-9947-1935-1501796-2
• [11] G. Fichtenholz and L. Kantorovich, Sur les opérations dans l'espace des functions bornées, Studia Mathematica, vol. 5 (1934), pp. 69-98.
• [12] I. Gelfand, Abstrakte Funktionen und lineare Operatoren, Recueil Mathématique, (n.s.), vol. 4 (1938), pp. 235-284.
• [13] M. Gowurin, Über die Stieltjiesche Integration abstrakter Funktionen, Fundamenta Mathematicae, vol. 27 (1936), pp. 254-268.
• [14] Hugh J. Hamilton, Transformations of multiple sequences, Duke Math. J. 2 (1936), no. 1, 29–60. MR 1545904, http://dx.doi.org/10.1215/S0012-7094-36-00204-1
• [15] T. H. Hildebrandt, On uniform limitedness of sets of functional operations, Bulletin of the American Mathematical Society, vol. 29 (1923), pp. 303-315.
• [16] J. D. Hill, A theorem in the theory of summability, Bull. Amer. Math. Soc. 42 (1936), no. 4, 225–228. MR 1563274, http://dx.doi.org/10.1090/S0002-9904-1936-06273-7
• [17] J. D. Hill and H. J. Hamilton, Operation theory and multiple sequence transformations, Duke Math. J. 8 (1941), 154–162. MR 0003827 (2,278b)
• [18] H. Löwig, Über die Dimension linearen Räume, Studia Mathematica, vol. 5 (1934), pp. 18-23.
• [19] E. H. Moore and H. L. Smith, A general theory of limits, American Journal of Mathematics, vol. 44 (1922), pp. 101-121.
• [20] J. von Neumann, Zur Algebra der Funktionaloperatioren und Theorie der normalen Operatoren, Mathematische Annalen, vol. 102 (1929-1930), pp. 913-944.
• [21] B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 277–304. MR 1501970, http://dx.doi.org/10.1090/S0002-9947-1938-1501970-8
• [22] R. S. Phillips, Integration in a convex linear topological space, Trans. Amer. Math. Soc. 47 (1940), 114–145. MR 0002707 (2,103c), http://dx.doi.org/10.1090/S0002-9947-1940-0002707-3
• [23] 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
• [24] G. Baley Price, The theory of integration, Trans. Amer. Math. Soc. 47 (1940), 1–50. MR 0001442 (1,239d), http://dx.doi.org/10.1090/S0002-9947-1940-0001442-5
• [25] A. E. Taylor, The weak topologies of Banach spaces, Proc. Nat. Acad. Sci. U. S. A. 25 (1939), 438–440. MR 0000652 (1,108c)
• [26] O. Toeplitz, Über allgemeine lineare Mittelbildungen, Prace Matematycznofizvczne, vol. 22 (1911), pp. 113-119.
• [27] John W. Tukey, Convergence and Uniformity in Topology, Annals of Mathematics Studies, no. 2, Princeton University Press, Princeton, N. J., 1940. MR 0002515 (2,67a)
• [28] B. Vulich, Sur les methodes linéares de sommation dans les espaces abstraits, Communications of the Institute of Mathematical and Mechanical Sciences of the University of Kharkhov and of the Mathematical Society of Kharkhov, (4), vol. 15 (1938).
• [29] John V. Wehausen, Transformations in linear topological spaces, Duke Math. J. 4 (1938), no. 1, 157–169. MR 1546041, http://dx.doi.org/10.1215/S0012-7094-38-00412-0

Bibliography

[1]

L. Alaoglu, Weak topologies in normed linear spaces, Annals of Mathematics, (2), vol. 41 (1940), pp. 252-267. MR 0001455 (1:241e)

[2]

P. Alexandroff and H. Hopf, Topologie I, Berlin, 1935.

[3]

S. Banach, Théorie des Opérations Linéares, Warsaw, 1932.

[4]

G. Birkhoff, Integration of functions with values in a Banach space, these Transactions, vol. 38 (1935), pp. 357-378. MR 1501815

[5]

-, Moore-Smith convergence in general topology, Annals of Mathematics, (2), vol. 38 (1937), pp. 39-56. MR 1503323

[6]

S. Bochner, Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind, Fundamenta Mathematicae, vol. 20 (1933), pp. 262-276.

[7]

S. Bochner and A. E. Taylor, Linear functionals on certain spaces of abstractly-valued functions, Annals of Mathematics, (2), vol. 39 (1938), pp. 913-944. MR 1503445

[8]

M. M. Day, Regularity of function-to-function transformations, Bulletin of the American Mathematical Society, vol. 45 (1939), pp. 296-303. MR 1563970

[9]

-, Reflexive Banach spaces not isomorphic to uniformly convex spaces, Bulletin of the American Mathematical Society, vol. 47 (1941), pp. 313-317. MR 0003446 (2:221b)

[10]

N. Dunford, Integration in general analysis, these Transactions, vol. 37 (1935), pp. 441-453. MR 1501796

[11]

G. Fichtenholz and L. Kantorovich, Sur les opérations dans l'espace des functions bornées, Studia Mathematica, vol. 5 (1934), pp. 69-98.

[12]

I. Gelfand, Abstrakte Funktionen und lineare Operatoren, Recueil Mathématique, (n.s.), vol. 4 (1938), pp. 235-284.

[13]

M. Gowurin, Über die Stieltjiesche Integration abstrakter Funktionen, Fundamenta Mathematicae, vol. 27 (1936), pp. 254-268.

[14]

H. J. Hamilton, Transformations of multiple sequences, Duke Mathematical Journal, vol. 2 (1936), pp. 29-60. MR 1545904

[15]

T. H. Hildebrandt, On uniform limitedness of sets of functional operations, Bulletin of the American Mathematical Society, vol. 29 (1923), pp. 303-315.

[16]

J. D. Hill, A theorem in the theory of summability, Bulletin of the American Mathematical Society, vol. 42 (1936), pp. 225-228. MR 1563274

[17]

J. D. Hill and H. J. Hamilton, Operation theory and multiple sequence transformations, Duke Mathematical Journal, vol. 8 (1941), pp. 154-162. MR 0003827 (2:278b)

[18]

H. Löwig, Über die Dimension linearen Räume, Studia Mathematica, vol. 5 (1934), pp. 18-23.

[19]

E. H. Moore and H. L. Smith, A general theory of limits, American Journal of Mathematics, vol. 44 (1922), pp. 101-121.

[20]

J. von Neumann, Zur Algebra der Funktionaloperatioren und Theorie der normalen Operatoren, Mathematische Annalen, vol. 102 (1929-1930), pp. 913-944.

[21]

B. J. Pettis, On integration in vector spaces, these Transactions, vol. 44 (1938), pp. 277-304. MR 1501970

[22]

R. S. Phillips, Integration in a convex linear topological space, these Transactions, vol. 47 (1940), pp. 114-145. MR 0002707 (2:103c)

[23]

-, On linear transformations, these Transactions, vol. 48 (1940), pp. 516-541. MR 0004094 (2:318c)

[24]

G. B. Price, The theory of integration, these Transactions, vol. 47 (1940), pp. 1-50. MR 0001442 (1:239d)

[25]

A. E. Taylor, The weak topologies of Banach spaces, Proceedings of the National Academy of Sciences, vol. 25 (1939), pp. 438-440. MR 0000652 (1:108c)

[26]

O. Toeplitz, Über allgemeine lineare Mittelbildungen, Prace Matematycznofizvczne, vol. 22 (1911), pp. 113-119.

[27]

J. W. Tukey, Convergence and Uniformity in Topology, Princeton, 1940. MR 0002515 (2:67a)

[28]

B. Vulich, Sur les methodes linéares de sommation dans les espaces abstraits, Communications of the Institute of Mathematical and Mechanical Sciences of the University of Kharkhov and of the Mathematical Society of Kharkhov, (4), vol. 15 (1938).

[29]

J. V. Wehausen, Transformations in linear topological spaces, Duke Mathematical Journal, vol. 4 (1938), pp 157-168. MR 1546041