On linear transformations

On linear transformations
HTML articles powered by AMS MathViewer

Trans. Amer. Math. Soc. 48 (1940), 516-541

DOI: https://doi.org/10.1090/S0002-9947-1940-0004094-3

PDF | Request permission

References

Théorie des Opérations Linéaires

Zur Theorie der linearen Dimension

Garrett Birkhoff, Integration of functions with values in a Banach space, Trans. Amer. Math. Soc. 38 (1935), no. 2, 357–378. MR 1501815, DOI 10.1090/S0002-9947-1935-1501815-3
S. Bochner, Additive set functions on groups, Ann. of Math. (2) 40 (1939), 769–799. MR 669, DOI 10.2307/1968893
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, DOI 10.2307/1968472
Nelson Dunford, Integration and linear operations, Trans. Amer. Math. Soc. 40 (1936), no. 3, 474–494. MR 1501886, DOI 10.1090/S0002-9947-1936-1501886-5
Nelson Dunford, Uniformity in linear spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 305–356. MR 1501971, DOI 10.1090/S0002-9947-1938-1501971-X
Nelson Dunford, A mean ergodic theorem, Duke Math. J. 5 (1939), 635–646. MR 98
Nelson Dunford and B. J. Pettis, Linear operations among summable functions, Proc. Nat. Acad. Sci. U.S.A. 25 (1939), 544–550. MR 343, DOI 10.1073/pnas.25.10.544

Sur les opérations linéaires dans l’espace des functions bornées

Les ensembles abstraits et le calcul fonctionnel

Abstrakte Funktionen und lineare Operatoren

Stieltjessche integration

T. H. Hildebrandt, On bounded linear functional operations, Trans. Amer. Math. Soc. 36 (1934), no. 4, 868–875. MR 1501772, DOI 10.1090/S0002-9947-1934-1501772-9
T. H. Hildebrandt and I. J. Schoenberg, On linear functional operations and the moment problem for a finite interval in one or several dimensions, Ann. of Math. (2) 34 (1933), no. 2, 317–328. MR 1503109, DOI 10.2307/1968205
Shizuo Kakutani, Iteration of linear operations in complex Banach spaces, Proc. Imp. Acad. Tokyo 14 (1938), no. 8, 295–300. MR 1568516

Sur la représentation des opérations linéaires

Über Kompaktheit der Funktionenmengen bei der Konvergenz im Mittel

Ingo Maddaus, On completely continuous linear transformations, Bull. Amer. Math. Soc. 44 (1938), no. 4, 279–282. MR 1563725, DOI 10.1090/S0002-9904-1938-06744-4
E. H. Moore and H. L. Smith, A General Theory of Limits, Amer. J. Math. 44 (1922), no. 2, 102–121. MR 1506463, DOI 10.2307/2370388

Beiträge zur Theorie der Orthogonalentwicklungen

B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 277–304. MR 1501970, DOI 10.1090/S0002-9947-1938-1501970-8
R. S. Phillips, Integration in a convex linear topological space, Trans. Amer. Math. Soc. 47 (1940), 114–145. MR 2707, DOI 10.1090/S0002-9947-1940-0002707-3

Theorie und Anwendung der absolut additiven Mengenfunktionen

Sur les ensembles compacts de fonctions sommables

J. D. Tamarkin, On the compactness of the space $L_p$, Bull. Amer. Math. Soc. 38 (1932), no. 2, 79–84. MR 1562331, DOI 10.1090/S0002-9904-1932-05332-0

Zur Kompaktheit im Raum ${L^p}$ für

Kôsaku Yosida, Mean ergodic theorem in Banach spaces, Proc. Imp. Acad. Tokyo 14 (1938), no. 8, 292–294. MR 1568515