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arXiv · 1407.7160

On extensions of $J$-skew-symmetric and $J$-isometric operators

Sergey M. Zagorodnyuk
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Abstract

In this paper it is proved that each densely defined $J$-skew-symmetric operator (or each $J$-isometric operator with $\overline{D(A)}=\overline{R(A)}=H$) in a Hilbert space $H$ has a $J$-skew-self-adjoint (respectively $J$-unitary) extension in a Hilbert space $\widetilde H\supseteq H$. We follow the ideas of Galindo in~[A.~Galindo, On the existence of $J$-self-adjoint extensions of $J$-symmetric operators with adjoint, Communications on pure and applied mathematics, Vol. XV, 423-425 (1962)] with necessary modifications.

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Sergey M. Zagorodnyuk. 2014-07-26. On extensions of $J$-skew-symmetric and $J$-isometric operators. https://arxiv.org/abs/1407.7160

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