Geodesic
Ultrametric spaces and related Hilbert spaces
Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 223-237

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We present simple proofs of the possibility of embedding ultrametric spaces in Hilbert spaces. The main part of the paper deals with ultrametric spaces that we call totally infinite spaces. Related Hilbert spaces, automorphisms of totally infinite spaces, and the corresponding linear operators are considered. 
@article{MZM_1997_62_2_a6,
     author = {R. S. Ismagilov},
     title = {Ultrametric spaces and related {Hilbert} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {223--237},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a6/}
}
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R. S. Ismagilov. Ultrametric spaces and related Hilbert spaces. Matematičeskie zametki, Tome 62 (1997) no. 2, pp. 223-237. http://geodesic.mathdoc.fr/item/MZM_1997_62_2_a6/