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The product of strong operator measurable functions is strong operator measurable

Author: G. W. Johnson
Journal: Proc. Amer. Math. Soc. 117 (1993), 1097-1104
MSC: Primary 46G10; Secondary 28B05, 28C15, 47A99
MathSciNet review: 1123654
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Abstract: Let $ {f_1}, \ldots ,{f_n}$ be strong operator measurable functions with values in the space of bounded linear operators on a separable Hilbert space. We show that the product $ {f_1} \cdots {f_n}$ is also strong operator measurable.

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  • [1] Donald L. Cohn, Measure theory, Birkhäuser, Boston, Mass., 1980. MR 578344
  • [2] Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
  • [3] Richard P. Feynman, An operator calculus having applications in quantum electrodynamics, Physical Rev. (2) 84 (1951), 108–128. MR 0044379
  • [4] G. W. Johnson, A bounded convergence theorem for the Feynman integral, J. Math. Phys. 25 (1984), no. 5, 1323–1326. MR 745743,
  • [5] Gerald W. Johnson and Michel L. Lapidus, Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman’s operational calculus, Mem. Amer. Math. Soc. 62 (1986), no. 351, vi+78. MR 849943,
  • [6] G. W. Johnson and D. L. Skoug, A Banach algebra of Feynman integrable functionals with application to an integral equation formally equivalent to Schroedinger’s equation, J. Functional Analysis 12 (1973), 129–152. MR 0348072
  • [7] G. W. Johnson and D. L. Skoug, The Cameron-Storvick function space integral: an 𝐿(𝐿_{𝑝},𝐿_{𝑝’}) theory, Nagoya Math. J. 60 (1976), 93–137. MR 0407228
  • [8] G. W. Johnson and D. L. Skoug, Stability theorems for the Feynman integral, Proceedings of the conference commemorating the 1st centennial of the Circolo Matematico di Palermo (Italian) (Palermo, 1984), 1985, pp. 361–377. MR 881415
  • [9] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
  • [10] Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959
  • [11] Laurent Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1973. Tata Institute of Fundamental Research Studies in Mathematics, No. 6. MR 0426084

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Keywords: Strong operator measurability, strong operator continuity, Souslin space, Radon measure, Lusin $ \mu $-measurability
Article copyright: © Copyright 1993 American Mathematical Society

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