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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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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/

[1] Vestfrid I. A., Timan A. F., “Ob odnom svoistve universalnosti gilbertovykh prostranstv”, Dokl. AN SSSR, 246:3 (1979), 528–530 | MR | Zbl

[2] Vestfrid I. A., “Ob universalnykh ultrametricheskikh prostranstvakh”, Ukr. matem. zh., 46:12 (1994), 1700–1706 | MR | Zbl

[3] Ismagilov R. S., “O neprivodimykh predstavleniyakh diskretnoi gruppy $\mathrm{SL}_2(\mathbb P)$, unitarnykh v indefinitnoi metrike”, Izv. AN SSSR. Ser. matem., 30:4 (1966), 923–950 | MR | Zbl

[4] Ismagilov R. S., “Elementarnye sfericheskie funktsii na gruppe $\mathrm{SL}_2(\mathbb P)$ nad polem, ne yavlyayuschimsya lokalno kompaktnym”, Izv. AN SSSR. Ser. matem., 31:2 (1967), 361–390 | MR | Zbl

[5] Ismagilov R. S., “O lineinykh predstavleniyakh grupp matrits s elementami iz normirovannogo polya”, Izv. AN SSSR. Ser. matem., 33:6 (1969), 1296–1323 | MR | Zbl

[6] Ismagilov R. S., “O predstavleniyakh $\mathrm{SL}_2(\mathbb P)$, gde $\mathbb P$ ne lokalno kompaktno”, Funktsion. analiz i ego prilozh., 7:4 (1973), 85–86 | MR | Zbl

[7] Timan A. F., “Ob approksimativnykh kharakteristikakh metricheskikh prostranstv i priblizhenii funktsii”, Tr. MIAN, 134, Nauka, M., 1975, 314–326 | MR | Zbl