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Differential geometry in the space of positive operators. (Spanish) Zbl 1028.58003

From the (Spanish) abstract: In [Integral Equations Oper. Theory 16, No. 3, 333-359 (1993; Zbl 0786.58006)] G. Corach, H. Porta and L. Recht studied the space of invertible, symmetric operators, particularly positive invertible operators from the point of view of the geometry of homogeneous spaces. This study continues at present, and it has produced some intersting results which are described in this paper.
The general reference of the concept of \(C^*\)-algebras is the book ‘Fundamentals of the theory of operator algebras. Vol. 1 (1983; Zbl 0518.46046) by R. V. Kadison and J. R. Ringrose.

MSC:

58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
46L05 General theory of \(C^*\)-algebras
46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory
47L99 Linear spaces and algebras of operators
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