A REFINED POLAR DECOMPOSITION FOR J-UNITARY OPERATORS

DOI10.5644/SJM.11.1.05zbMATH Open1325.47005arXiv1408.3687MaRDI QIDQ3447520

S. M. Zagorodnyuk

Publication date: 27 October 2015

Published in: SARAJEVO JOURNAL OF MATHEMATICS (Search for Journal in Brave)

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 $finD(A)$ implies $JfinD(A)$ and $AJf=-JAf$, where $J$ is a conjugation on $H$).

Full work available at URL: https://arxiv.org/abs/1408.3687

zbMATH Keywords

polar decompositionconjugationsymmetric operator\(J\)-unitary operator

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Dilations, extensions, compressions of linear operators (47A20) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items (2)

A unitary Susskind–Glogower operator based on polarization ⋮ On the structure of real operators

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