×

Notes on the bicategory of \(\mathrm{W}^\ast\)-bimodules. (English) Zbl 1435.46045

Summary: Categories of \(\mathrm{W}^\ast\)-bimodules are shown in an explicit and algebraic way to constitute an involutive \(\mathrm{W}^\ast\)-bicategory.

MSC:

46L10 General theory of von Neumann algebras
18N10 2-categories, bicategories, double categories
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
PDF BibTeX XML Cite
Full Text: DOI arXiv Euclid

References:

[1] M. Baillet, Y. Denizeau and J. F. Havet, Indice d’une espĂ©rance conditionnelle, Compositio Math., 66 (1988), 199-236. · Zbl 0657.46041
[2] J. W. Barrett and B. W. Westbury, Spherical categories, Adv. Math., 143 (1999), 357-375. · Zbl 0930.18004
[3] P. Ghez, R. Lima and J. E. Roberts, W*-categories, Pacific J. Math., 120 (1985), 79-109.
[4] U. Haagerup, The standard form of von Neumann algebras, Math. Scand., 37 (1975), 271-283. · Zbl 0304.46044
[5] S. MacLane, Categories for the working mathematician, Second edition, Springer-Verlag, 1998. · Zbl 0705.18001
[6] J. L. Sauvageot, Sur le produit tensoriel relatif d’espaces de Hilbert, J. Operator Theory, 9 (1983), 237-252. · Zbl 0517.46050
[7] M. Takesaki, Theory of Operator Algebras, II, Encyclopaedia of Mathematical Sciences, 125, Springer-Verlag, 2003. · Zbl 1059.46031
[8] A. Thom, A remark about Connes fusion tensor product, Theory Appl. Categ., 25 (2011), 38-50. · Zbl 1227.46045
[9] S. Yamagami, Algebraic aspects in modular theory, Publ. Res. Inst. Math. Sci., 28 (1992), 1075-1106. · Zbl 0809.46075
[10] S. Yamagami, Modular theory for bimodules, J. Funct. Anal., 125 (1994), 327-357. · Zbl 0816.46043
[11] S. Yamagami, Frobenius duality in \(C^*\)-tensor categories, J. Operator Theory, 52 (2004), 3-20. · Zbl 1078.46045
[12] S. Yamagami, Notes on operator categories, J. Math. Soc. Japan, 59 (2007), 541-555. · Zbl 1126.46049
[13] S. Yamagami, Around trace formulas in non-commutative integration, Publ. Res. Inst. Math. Sci., 54 (2018), 181-211. · Zbl 1419.46039
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.