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References
C. J. Atkin,The Finsler geometry of groups of isometries of Hilbert space, J. Australian Math. Soc., 42 (1987), 196–222
C. J. Atkin,The Finsler geometry of certain covering groups of operator groups, Hokkaido Math. J., 18 (1989), 45–77.
J. Cheeger and D. Gromoll,On the structure of complete manifolds of non-negative curvature, Annals of Mathematics, (2) 96 (1972), 413–443.
G. Corach, H. Porta, and L. Recht,An Operator Inequality, Linear Algebra and its Applications, 142 (1990) 153–158.
G. Corach, H. Porta, and L. Recht,Differential Geometry of Systems of Projections in Banach Algebras, Pacific Journal of Mathematics, 143 (1990), 209–228.
G. Corach, H. Porta, and L. Recht,The Geometry of Spaces of Projections in C *-Algebras, to appear in Advances in Mathematics.
G. Corach, H. Porta, and L. Recht,A geometric interpretation of Segal's inequality ‖eX+Y‖≤‖eX/2eYeX/2‖. To appear in Proc. Amer. Math. Soc.
G. Corach, H. Porta, and L. Recht,Differential Geometry of Spaces of Relatively Regular Operators, Integral Equations and Operator Theory, 13 (1990) 771–794.
Ju. L. Daleckii,Properties of Operators depending on a parameter, Dopovidi. Akad. Nauk. Ukrain. RSR, 6 (1950), 433–436 (Ukrainian)
Ju. L. Daleckii and S. G. Krein,Stability of Solutions of Differential Equations in Banach Spaces, Trans. Math. Monographs 43, AMS, Providence, 1974
J. D. Dollard and C. N. Friedman,Product Integration, Encyclopedia of Mathematics and its Applications, Vol 10, Addison-Wesley, 1979.
P. de la Harpe,Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space, Lecture Notes in Mathematics Nr. 285, Springer-Verlag, 1972
P. de la Harpe,Initiation à l'algèbre de Calkin, Algèbres d'opérateurs, Lecture Notes in Mathematics Nr. 725, pp. 180–219, Springer-Verlag, 1979
T. Kato,On the Adiabatic Theorem of Quantum Mechanics, J. Phys. Soc. Japan 5 (1950), 435–439.
T. Kato, “Perturbation Theory for Linear Operators”, 2nd Ed., Springer-Verlag, Berlin, 1984.
E. Michael,Convex structures and continuous selections, Canad. J. Math., 4 (1959), 556–575
H. Porta and L. Recht,Spaces of Projections in Banach Algebras, Acta Matemática Venezolana, 38 (1987), 408–426.
H. Porta and L. Recht,Minimality of Geodesics in Grassmann Manifolds, Proc. AMS 100 (1987), 464–466.
V. P. Potapov,The multiplicative structure of J-contractive matrix functions (Appendix), Amer. Math. Soc. Transl., Ser II, 15, (1960), 131–244.
C. E. Rickart, “General Theory of Banach Algebras”, Van Nostrand, New York, 1960
I. Segal,Notes toward the construction of nonlinear relativistic quantum fields, Bull. Amer. Math. Soc., 75 (1969), 1390–1395
V. Volterra et A. Hostinsky, Opérations infinitesimales linéaires, Gauthier-Villars, Paris, 1938.
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Research partially supported by CONICET, Argentina and by Fundacion Antorchas, Argentina.
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Corach, G., Porta, H. & Recht, L. The geometry of the space of selfadjoint invertible elements in a C*-algebra. Integr equ oper theory 16, 333–359 (1993). https://doi.org/10.1007/BF01204226
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DOI: https://doi.org/10.1007/BF01204226