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arXiv · 1711.08787

Operator least squares problems and Moore-Penrose inverses in Krein spaces

Maximiliano Contino·Alejandra Maestripieri·Stefania Marcantognini
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Abstract

A Krein space H and bounded linear operators B, C on H are given. Then, some min and max problems about the operators (BX - C)^{#}(BX -C), where X runs over the space of all bounded linear operators on H, are discussed. In each case, a complete answer to the problem, including solvability conditions and characterization of the solutions, is presented. Also, an adequate decomposition of B is considered and the min-max problem is addressed. As a by-product the Moore-Penrose inverse of B is characterized as the only solution of a variational problem. Other generalized inverses are described in a similar fashion as well.

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Maximiliano Contino, Alejandra Maestripieri, Stefania Marcantognini. 2017-11-23. Operator least squares problems and Moore-Penrose inverses in Krein spaces. https://arxiv.org/abs/1711.08787

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