Finite-Dimensional Extensions of Certain Symmetric Operators(1)
Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 455-456
Voir la notice de l'article provenant de la source Cambridge University Press
Let H be a Hilbert space with inner product 〈,). A well-known theorem of von Neumann states that, if S is a symmetric operator in H, then S has a selfadjoint extension in H if and only if S has equal deficiency indices. This result was extended by Naimark, who proved that, even if the deficiency indices of S are unequal, there always exists a Hilbert space H1 such that H ⊆ H1 and S has a selfadjoint extension in H1.
Michael, I. M. Finite-Dimensional Extensions of Certain Symmetric Operators(1). Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 455-456. doi: 10.4153/CMB-1973-076-6
@article{10_4153_CMB_1973_076_6,
author = {Michael, I. M.},
title = {Finite-Dimensional {Extensions} of {Certain} {Symmetric} {Operators(1)}},
journal = {Canadian mathematical bulletin},
pages = {455--456},
year = {1973},
volume = {16},
number = {3},
doi = {10.4153/CMB-1973-076-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-076-6/}
}
TY - JOUR AU - Michael, I. M. TI - Finite-Dimensional Extensions of Certain Symmetric Operators(1) JO - Canadian mathematical bulletin PY - 1973 SP - 455 EP - 456 VL - 16 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-076-6/ DO - 10.4153/CMB-1973-076-6 ID - 10_4153_CMB_1973_076_6 ER -
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