References
[BS] Bennett, C., Sharpley, R.: Interpolation of Operators. Orland, Florida: Academic Press 1988
[CR] Chong, K.M., Rice, N.M.: Equimeasurable rearrangements of functions. (Queen's Pap. Pure Appl. Math., no. 28) Kingston: Queen's University 1971
[DP] Doods, P.G., de Pagter, B.: Non-commutative Banach function spaces and their duals. Semester Bericht Funktionanalysis. Tübingen, Wintersemester (1988)
[DDP] Doods, P.G., Doods, T.K.-Y., de Pagter, B.: Non-commutative Banach function spaces. Math. Z.201, 583–597 (1989)
[FK] Fack, T., Kosaki, H.: Generalizeds-numbers of τ-measurable operators. Pac. J. Math.123, 269–300 (1986)
[GK] Gohberg, I.C., Krein, M.G.: Introduction to the theory of linear non-selfadjoint operators. (Transl. Math. Monogr., vol. 18) Providence, RI: Am. Math. Soc. 1969
[H] Hiai, F.: Majorization and stochastic maps in von Neumann algebras. J. Math. Anal. Appl.127, 18–48 (1987)
[HN1] Hiai, F., Nakamura, Y.: Majorizations for generalizeds-numbers in semifinite von Neumann algebras. Math. Z.195, 17–27 (1987)
[HN2] Hiai, F., Nakamura, Y.: Distance between unitary orbits in von Neumann algebras. Pac. J. Math.138, 259–294 (1989)
[K] Kosaki, H.: Non-commutative Lorentz spaces associated with a semifinite von Neumann algebra and applications. Proc. Japan Acad. Ser. A57, 303–306 (1981)
[L] Luxemburg, W.A.J.: Rearrangement invariant Banach function spaces. (Queen's Pap. Pure Appl. Math., no. 10, pp. 83–144) Kingston: Queen's University 1967
[LS] Lorentz, G.G., Shimogaki, T.: Interpolation theorems for operators in function spaces. J. Funct. Anal.2, 31–51 (1968)
[N] Nelson, E.: Notes on non-commutative integration. J. Funct. Anal.15, 103–116 (1974)
[O] Ovchinnikov, V.I.:s-numbers of measurable operators. Funct. Anal. Appl.4, 236–242 (1970)
[Ta] Takesaki, M.: Theory of Operator Algebras I. Berlin Heidelberg New York: Springer 1979
[Te] Terp, M.:L p-spaces associated with von Neumann algebras. Notes, Copenhagen University (1981)
[Ti] Tikhonov, O.E.: Continuity of operator functions in topologies connected with a trace on a von Neumann algebra (in Russian). Izv. Vyssh. Uchebn. Zaved. Mat.1, 77–79 (1987); translated in Sov. Math.31, 110–114 (1987)
[W] Watanabe, K.: Finiteness of von Neumann algebras and non-commutativeL p-spaces. Hokkaido Math. J.19, 297–305 (1990)
[Y1] Yeadon, F.J.: Non-commutativeL p-spaces. Math. Proc. Camb. Philos. Soc.77, 91–102 (1975)
[Y2] Yeadon, F.J.: Ergodic theorems for semifinite von Neumann algebras II. Math. Proc. Camb. Philos. Soc.88, 135–147 (1980)
Author information
Authors and Affiliations
Additional information
Supported in part by a Grant-in-aid for Scientific Research from the Japanese Ministry of Education
Rights and permissions
About this article
Cite this article
Watanabe, K. Some results on non-commutative Banach function spaces. Math Z 210, 555–572 (1992). https://doi.org/10.1007/BF02571813
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02571813