Isometries of 𝐿_{𝑝}-spaces associated with semifinite von Neumann algebras

Tam, P. K.

doi:10.1090/S0002-9947-1979-0539922-3

Isometries of $L_{p}$-spaces associated with semifinite von Neumann algebras
HTML articles powered by AMS MathViewer

by P. K. Tam PDF

Trans. Amer. Math. Soc. 254 (1979), 339-354 Request permission

Abstract:

The paper determines the structure of (classes of) linear isometries between ${L_p}$-spaces associated with semifinite normal faithful traces on von Neumann algebras, generalizing works of M. Broise and B. Russo. Also established are some auxiliary results on ${L_p}$ norm inequalities which are of interest by themselves.

References

J. Dixmier, Formes linéaires sur un anneau d’opérateurs, Bull. Soc. Math. France 81 (1953), 9–39 (French). MR 59485, DOI 10.24033/bsmf.1436
I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. (2) 57 (1953), 401–457. MR 54864, DOI 10.2307/1969729
R. A. Kunze, $L_{p}$ Fourier transforms on locally compact unimodular groups, Trans. Amer. Math. Soc. 89 (1958), 519–540. MR 100235, DOI 10.1090/S0002-9947-1958-0100235-1
Tôzirô Ogasawara and Kyôichi Yoshinaga, A noncommutative theory of integration for operators, J. Sci. Hiroshima Univ. Ser. A 18 (1955), 311–347. MR 70989
Bernard Russo, Isometrics of $L^{p}$-spaces associated with finite von Neumann algebras, Bull. Amer. Math. Soc. 74 (1968), 228–232. MR 221294, DOI 10.1090/S0002-9904-1968-11898-1
Michel Broise, Sur les isomorphismes de certaines algèbres de von Neumann, Ann. Sci. École Norm. Sup. (3) 83 (1966), 91–111 (French). MR 0213885, DOI 10.24033/asens.1149
John Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459–466. MR 105017, DOI 10.2140/pjm.1958.8.459
Tosio Kato, Perturbation theory for linear operators, 2nd ed., Grundlehren der Mathematischen Wissenschaften, Band 132, Springer-Verlag, Berlin-New York, 1976. MR 0407617

Les algèbres d’opérateurs dans l’espace Hilbertien

J. Dixmier, Applications $\natural$ dans les anneaux d’opérateurs, Compositio Math. 10 (1952), 1–55 (French). MR 51443
Richard V. Kadison, Isometries of operator algebras, Ann. of Math. (2) 54 (1951), 325–338. MR 43392, DOI 10.2307/1969534
Charles A. McCarthy, $c_{p}$, Israel J. Math. 5 (1967), 249–271. MR 225140, DOI 10.1007/BF02771613