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arXiv · 0910.2599

On a J-polar decomposition of a bounded operator and matrix representations of J-symmetric, J-skew-symmetric operators

Sergey M. Zagorodnyuk
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Abstract

In this work a possibility of a decomposition of a bounded operator which acts in a Hilbert space $H$ as a product of a J-unitary and a J-self-adjoint operators is studied, $J$ is a conjugation (an antilinear involution). Decompositions of J-unitary and unitary operators which are analogous to decompositions in the finite-dimensional case are obtained. A possibility of a matrix representation for J-symmetric, J-skew-symmetric operators is studied. Also, some simple properties of J-symmetric, J-antisymmetric, J-isometric operators are obtained, a structure of a null set for a J-form is studied.

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Sergey M. Zagorodnyuk. 2009-10-14. On a J-polar decomposition of a bounded operator and matrix representations of J-symmetric, J-skew-symmetric operators. https://arxiv.org/abs/0910.2599

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