arXiv subjects

Tiberiu Constantinescu

Publications and source records attributed to Tiberiu Constantinescu.

3 recordsLinked to original sources

arXiv2018

Notes on (the Birmak-Krein-Vishik theory on) selfadjoint extensions of semibounded symmetric operators

We give an explicit and versatile parametrization of all positive selfadjoint extensions of a densely defined, closed, positive operator. In addition, we identify the Friedrichs extension by specifying the parameter to which it corresponds. This is a manuscript that was circulated as the first part of the preprint "Two papers on selfadjoint extensions of symmetric semibounded operators", INCREST Preprint Series, July 1981, Bucharest, Romania, but never published. In this LaTeX typeset version, only typos and a few inappropriate formulations have been corrected, with respect to the original manuscript. I decided to post it on arXiv since, taking into account recent articles, the results are still of current interest. Tiberiu Constantinescu died in 2005.

math.FA↗

arXiv2002

Note on purifications of a qubit

This work provides a parametrization of the set of purifications of a 2x2 mixed state, and joint purifications (if any) of a given pair of mixed 2x2 states. The former is parametrized by SO(3, R), while the latter is parametrized by SO(2,R), except when the 2x2 state is pure. Using this parametrization some quantum information measures are obtained. In the process it is shown how to solve one variation of the classical Procustes problem. The appendix is devoted to the first step in extending this work to higher dimensions.

quant-ph↗

arXiv2000

Representations of hermitian kernels by means of Krein spaces II. Invariant kernels

In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels which realize the given action by bounded operators on a Krein space. Applications to the GNS representation of *-algebras associated to hermitian functionals are given. We explain the key role played by the Kolmogorov decomposition in the construction of Weyl exponentials associated to an indefinite inner product and in the dilation thoery of hermitian maps on C*-algebras.

math.FA↗