Geodesic
Positive Definite Sequence of Operators and a Fixed Point Theorem
Canadian mathematical bulletin, Tome 15 (1972) no. 2, p. 295

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this note is to prove the following:Theorem. Let {A n} be a positive definite sequence of operators on a Hilbert space H with A 0=1. If A1 f=f for some f in H, then A n f=f for all n.Note that a bilateral sequence of operators {An:n = 0, ±1, ±2,...} on H is positive definite if for every finitely nonzero sequence {fn} of vectors in H [1]. 
Dash, A. T. Positive Definite Sequence of Operators and a Fixed Point Theorem. Canadian mathematical bulletin, Tome 15 (1972) no. 2, p. 295. doi: 10.4153/CMB-1972-054-3
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[1] 1. Riesz, F. and Sz.-Nagy, B., Appendix to functional analysis, Ungar, New York. Google Scholar

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