On $J$-self-adjoint extensions of the Phillips symmetric operator

Abstract

$J$-self-adjoint extensions of the Phillips symmetric operator $S$ are studied. The concepts of stable and unstable $C$-symmetry are introduced in the extension theory framework. The main results are the following: if $A$ is a $J$-self-adjoint extension of $S$, then either $\sigma (A)=\mathbb{R}$ or $\sigma (A)=\mathbb{C}$; if $A$ has a real spectrum, then $A$ has a stable $C$-symmetry and $A$ is similar to a self-adjoint operator; there are no $J$-self-adjoint extensions of the Phillips operator with unstable $C$-symmetry.

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Cited by in corpus (2)

• On J-Self-Adjoint Operators with Stable C-Symmetry
• On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl_2