Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 443-447
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H. Langer. On the maximal dual pairs of invariant subspaces of $J$-self-adjoint operators. Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 443-447. http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a8/
@article{MZM_1970_7_4_a8,
author = {H. Langer},
title = {On the maximal dual pairs of invariant subspaces of $J$-self-adjoint operators},
journal = {Matemati\v{c}eskie zametki},
pages = {443--447},
year = {1970},
volume = {7},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a8/}
}
TY - JOUR
AU - H. Langer
TI - On the maximal dual pairs of invariant subspaces of $J$-self-adjoint operators
JO - Matematičeskie zametki
PY - 1970
SP - 443
EP - 447
VL - 7
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a8/
LA - ru
ID - MZM_1970_7_4_a8
ER -
%0 Journal Article
%A H. Langer
%T On the maximal dual pairs of invariant subspaces of $J$-self-adjoint operators
%J Matematičeskie zametki
%D 1970
%P 443-447
%V 7
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a8/
%G ru
%F MZM_1970_7_4_a8
In the $J$-spaces $\mathfrak{H}=\mathfrak{H}_1\oplus\mathfrak{H}_2$, with the infinite-dimensional components $\mathfrak{H}_k=P_k\mathfrak{H}$ ($k=1,2$), we can always find an operator $A$, for which there are at least two distinct invariant maximal dual pairs, such that if $[x,x]=0$ and $[Ax,x]=0$, then $x=0$.
