This article is cited in 3 papers

On the maximal dual pairs of invariant subspaces of $J$-self-adjoint operators

H. Langer

Dresden Technical University

Abstract: 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 $x=0$.

UDC: 513.88

Received: 17.03.1969

 English version: Mathematical Notes, 1970, 7:4, 269–271

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