Bilinear transformations in Hilbert space
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- by Francis J. Murray
- Trans. Amer. Math. Soc. 45 (1939), 474-507
- DOI: https://doi.org/10.1090/S0002-9947-1939-1501999-0
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References
- S. Banach, Théorie des Opérations Linéaires, Warsaw, 1932.
—, Studia Mathematica, vol. 8 (1938), pp. 36-44.
F. L. Hitchcock, Journal of Mathematics and Physics, vol. 8 (1929), p. 83. (This memoir contains references to preceding work on the finite dimensional case.)
M. Kerner, Annals of Mathematics, (2), vol. 41 (1937), pp. 208-248.
S. Mazur and W. Orlicz, Studia Mathematica, vol. 5 (1935), pp. 50-68, 179-189.
- F. J. Murray, Linear transformations between Hilbert spaces and the application of this theory to linear partial differential equations, Trans. Amer. Math. Soc. 37 (1935), no. 2, 301–338. MR 1501788, DOI 10.1090/S0002-9947-1935-1501788-3
- F. J. Murray and J. Von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), no. 1, 116–229. MR 1503275, DOI 10.2307/1968693 —, these Transactions, vol. 41 (1937), pp. 208-248. J. von Neumann, Mathematische Annalen, vol. 102 (1929-1930), pp. 370-427. —, Annals of Mathematics, (2), vol. 32 (1931), pp. 191-226. —, Annals of Mathematics, vol. 33 (1932), pp. 294-310. R. Oldenburger, Annals of Mathematics, (2), vol. 35 (1934), pp. 622-657 (two papers). —, these Transactions, vol. 39 (1936), pp. 422-455.
- Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877, DOI 10.1090/coll/015
Bibliographic Information
- © Copyright 1939 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 45 (1939), 474-507
- MSC: Primary 47A99; Secondary 46C05, 47B15, 47B25, 47L30
- DOI: https://doi.org/10.1090/S0002-9947-1939-1501999-0
- MathSciNet review: 1501999