Al-Rashed, Maryam H. A.; Zegarliński, Bogusław Noncommutative Orlicz spaces associated to a state. II. (English) Zbl 1221.46065 Linear Algebra Appl. 435, No. 12, 2999-3013 (2011). Summary: We introduce and study the noncommutative Orlicz spaces associated to a normal faithful state on a semifinite von Neumann algebra. We also prove some convergence theorems for the (unbounded) trace measurable operators.For Part I, cf.[Stud. Math. 180, No. 3, 199–209 (2007; Zbl 1126.46042)]. Cited in 1 ReviewCited in 5 Documents MSC: 46L52 Noncommutative function spaces 46L51 Noncommutative measure and integration 15A45 Miscellaneous inequalities involving matrices Keywords:noncommutative Orlicz spaces; semifinite von Neumann algebras; Young and Hölder inequalities; comparison of norms; quantum information geometry Citations:Zbl 1126.46042 PDFBibTeX XMLCite \textit{M. H. A. Al-Rashed} and \textit{B. Zegarliński}, Linear Algebra Appl. 435, No. 12, 2999--3013 (2011; Zbl 1221.46065) Full Text: DOI References: [1] Al-Rashed, M.; Zegarłiński, B., Noncommutaive Orlicz spaces associated with a state, Studia Math., 180, 199-209 (2007) · Zbl 1126.46042 [2] Akemann, C.; Anderson, J.; Pedersen, G., Triangle inequalities in operator algebras, Linear and Multilinear Algebra, 11, 167-178 (1982) · Zbl 0485.46029 [3] Araki, H.; Masuda, T., Positive cones and \(L_p -\) spaces for von Neumann algebras, Publ. RIMS Koyoto Univ., 18, 339-411 (1982) [4] Dixmier, J., Forms linéaires sur un anneau d’opératurs, Bull. Soc. Math. France, 81, 9-39 (1953) · Zbl 0050.11501 [5] Fack, T.; Kosaki, H., Generalised s-numbers of \(\tau \)-measurable operators, Pacific J. Math., 123, 269-300 (1986) · Zbl 0617.46063 [6] Kosaki, H., Application of the complex interpolation method to a von Neumann algebra (non-commutative \(L_p\)-spaces), J. Funct. Anal., 56, 29-78 (1984) · Zbl 0604.46063 [7] Kufner, A.; Fucik, S., Function Spaces (1977), Academia: Academia Prag [8] Kunze, W., Noncommutative Orlicz spaces and generalized Arens algebras, Mth. Nachr., 147, 123-138 (1990) · Zbl 0746.46062 [9] Muratov, M., Noncommutative Orlicz-spaces, Dokl. Akad. Nauk UzSSR, 6, 11-13 (1978) · Zbl 0467.46053 [10] Muratov, M., The Luxemburg norm in Orlicz-spaces, Dokl. Akad. Nauk. UzSSR, 1, 5-6 (1979) · Zbl 0467.46054 [11] Nelson, E., Notes on non-commutative integration, J. Funct. Anal., 15, 103-116 (1974) · Zbl 0292.46030 [12] Rao, M.; Ren, Z., Theory of Orlicz Spaces (1991), Marcel Dekker Inc.: Marcel Dekker Inc. New York · Zbl 0724.46032 [13] Segal, I. E., A non-commutative extension of abstract integration, Ann. Math., 57, 401-457 (1953) · Zbl 0051.34201 [14] Streater, R., Quantum Orlicz spaces in information geometry, Open Syst. Inf. Dyn., 11, 359-375 (2004), ArXiv:math-ph/0407046 · Zbl 1084.81024 [15] Takesaki, M., Theory of Operator Algebras II (2000), Springer, (Encyclopedia of Mathematical Sciences) · Zbl 0990.46034 [16] M. Terp, \( L_p\); M. Terp, \( L_p\) [17] Terp, M., Interpolation spaces between a von Neumann algebra and its dual, J. Operator Theory, 8, 327-360 (1982) · Zbl 0532.46035 [18] Trunov, N. V., On a noncommutative analogue of the space \(L_p\), Izvestiya VUZ. Matematika, 23, 69-77 (1979), (Soviet Math. Transl.) · Zbl 0429.46041 [19] Yeadon, F., Noncommutative \(L_p\)-spaces, Proc. Cambridge Philos. Soc., 77, 91-102 (1975) · Zbl 0327.46068 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.