Exponential arcs in the manifold of vector states on a $$\sigma $$-finite von Neumann algebra

Amari, S.: Differential-geometrical Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer, New York (1985)

Amari, S., Nagaoka, H.: Methods of Information Geometry (Oxford University Press, 2000) (Originally published in Japanese by Iwanami Shoten, Tokyo, Japan, 1993)

Amari, S.: Information Geometry and its Applications. Springer, New York (2016)

Ay, N., Jost, J., Vân Lê, H., Schwachhöfer, L.: Information Geometry. Springer, New York (2017)

Pistone, G., Sempi, C.: An infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one. Ann. Stat. 23, 1543–1561 (1995)

Gibilisco, P., Pistone, G.: Connections on nonparametric statistical manifolds by Orlicz space geometry. Infin. Dimens. Anal. Quant. Probab. Relat. Top. 1, 325–347 (1998)

Pistone, G.: Nonparametric information geometry. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information, pp. 5–36. Springer, New York (2013)

Pistone, G., Cena, A.: Exponential statistical manifold. AISM 59, 27–56 (2007)

Santacroce, M., Siri, P., Trivellato, B.: On mixture and exponential connection by open arcs. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information, pp. 577–584. Springer, New York (2017)

Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics I. Springer, New York (1979)

Petz, D.: Quantum Information Theory and Quantum Statistics. Springer, New York (2008)

Haag, R., Hugenholz, N.M., Winnink, M.: On the equilibrium states in quantum statistical mechanics. Commun. Math. Phys. 5, 215–236 (1967)

Takesaki, M.: Tomita’s Theory of Modular Hilbert Algebras and its Applications. Lecture Notes in Mathematics, vol. 128. Springer, New York (1970)

Araki, H.: Some properties of modular conjugation operator of von Neumann algebras and a non-commutative Radon–Nikodym theorem with a chain rule. Pac. J. Math 50, 309–354 (1974)

Grasselli, M.R., Streater, R.F.: On the uniqueness of the Chentsov metric in quantum information geometry. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4, 173–182 (2001)

Grasselli, M.R., Streater, R.F.: The quantum information bound for $$\epsilon $$-bounded forms. Rep. Math. Phys. 46, 325–335 (2000)

Streater, R.F.: Duality in quantum information geometry. Open Syst. Inf. Dyn. 11, 71–77 (2004)

Streater, R.F.: Quantum Orlicz Spaces in Information Geometry. Open Syst. Inf. Dyn. 2004(11), 359–375 (2004)

Jenčová, A.: Geometry of quantum states: dual connections and divergence functions. Rep. Math. Phys. 47, 121–138 (2001)

Jenčová, A.: A construction of a nonparametric quantum information manifold. J. Funct. Anal. 239, 1–20 (2006)

Kato, T.: Perturbation Theory for Linear Operators. Springer, New York (1966)

Ohara, A., Suda, N., Amari, S.: Dualistic differential geometry of positive definite matrices and its applications to related problems. Linear Algebra Appl. 247, 31–53 (1996)

Ohara, A.: Geodesics for dual connections and means on symmetric cones. Integr. Equ. Oper. Theory 50, 537–548 (2004)

Uohashi, K., Ohara, A.: Jordan algebra and dual affine connections on symmetric cones. Positivity 8, 369–378 (2004)

Ohara, A.: Doubly autoparallel structure on positive definite matrices and its applications. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information, pp. 251–260. Springer, New York (2019)

Uohashi, K.: $$\alpha $$-power sums on symmetric cones. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information, pp. 126–134. Springer, New York (2019)

Ciaglia, F.M., Ibort, A., Jost, J., Marmo, G.: Manifolds of classical probability distributions and quantum density operators in infinite dimensions. Inf. Geom. 2, 231–271 (2019)

Ciaglia, F.M., Jost, J., Schwachhöfer, L.: From the Jordan product to Riemannian geometries on classical and quantum states. Entropy 22(6), 637 (2020)

Ciaglia, F.M., Jost, J., Schwachhöfer, L.: Differential geometric aspects of parametric estimation theory for states on finite-dimensional $$C^*$$-algebras. Entropy 22(11), 1332 (2020)

Naudts, J.: Quantum statistical manifolds. Entropy 20, 472 (2018) [Correction Entropy 20, 796 (2018)]

Naudts, J.: Quantum statistical manifolds: the finite-dimensional case. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information, pp. 631–637. Springer, New York (2019)

Naudts, J.: Quantum statistical manifolds: the linear growth case. Rep. Math. Phys. 84, 151–169 (2019)

Newton, N.J.: An infinite-dimensional statistical manifold modeled on Hilbert space. J. Funct. Anal. 263, 1661–1681 (2012)

Newton, N.J.: A class of non-parametric statistical manifolds modelled on Sobolev space. Inf. Geom. 2, 283–312 (2019)

Montrucchio, L., Pistone, G.: Deformed exponential bundle: the linear growth case. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information, pp. 239–246. Springer, New York (2017)

Montrucchio, L., Pistone, G.: A class of non-parametric deformed exponential statistical models. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information, pp. 15–35. Springer, New York (2019)

Dixmier, J.: von Neumann Algebras. North-Holland, Amsterdam (1981)

Haagerup, U.: The standard form of von Neumann algebras. Math. Scand. 37, 271–283 (1975)

Rieffel, M.A., van Daele, A.: A bounded operator approach to Tomita–Takesaki theory. Pac. J. Math. 69, 187–221 (1977)