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arXiv · 1408.3687

A refined polar decomposition for $J$-unitary operators

Sergey M. Zagorodnyuk
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Abstract

In this paper, we shall characterize the components of the polar decomposition for an arbitrary $J$-unitary operator in a Hilbert space. This characterization has a quite different structure as that for complex symmetric and complex skew-symmetric operators. It is also shown that for a $J$-imaginary closed symmetric operator in a Hilbert space there exists a $J$-imaginary self-adjoint extension in a possibly larger Hilbert space (a linear operator $A$ in a Hilbert space $H$ is said to be $J$-imaginary if $f\in D(A)$ implies $Jf\in D(A)$ and $AJf = -JAf$, where $J$ is a conjugation on $H$).

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Sergey M. Zagorodnyuk. 2014-08-16. A refined polar decomposition for $J$-unitary operators. https://arxiv.org/abs/1408.3687

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