Geodesic
Operators on Anti-dual pairs: Self-adjoint Extensions and the Strong Parrott Theorem
Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 813-824

Voir la notice de l'article provenant de la source Cambridge

DOI

The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space structure or a normable topology. In fact, we will show how hermitian extensions of linear functionals of involutive algebras can be governed by means of their induced operators. As an operator theoretic application, we provide a direct generalization of Parrott’s theorem on contractive completion of 2 by 2 block operator-valued matrices. To exhibit the applicability in noncommutative integration, we characterize hermitian extendibility of symmetric functionals defined on a left ideal of a $C^{\ast }$-algebra.
DOI : 10.4153/S0008439520000065
Mots-clés : Self-adjoint operator, symmetric operator, anti-duality, self-adjoint extension, Parrott theorem, *-algebra, positive functional, hermitian functional 
Tarcsay, Zsigmond; Titkos, Tamás. Operators on Anti-dual pairs: Self-adjoint Extensions and the Strong Parrott Theorem. Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 813-824. doi: 10.4153/S0008439520000065
@article{10_4153_S0008439520000065,
     author = {Tarcsay, Zsigmond and Titkos, Tam\'as},
     title = {Operators on {Anti-dual} pairs: {Self-adjoint} {Extensions} and the {Strong} {Parrott} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {813--824},
     year = {2020},
     volume = {63},
     number = {4},
     doi = {10.4153/S0008439520000065},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000065/}
}
TY  - JOUR
AU  - Tarcsay, Zsigmond
AU  - Titkos, Tamás
TI  - Operators on Anti-dual pairs: Self-adjoint Extensions and the Strong Parrott Theorem
JO  - Canadian mathematical bulletin
PY  - 2020
SP  - 813
EP  - 824
VL  - 63
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000065/
DO  - 10.4153/S0008439520000065
ID  - 10_4153_S0008439520000065
ER  - 
%0 Journal Article
%A Tarcsay, Zsigmond
%A Titkos, Tamás
%T Operators on Anti-dual pairs: Self-adjoint Extensions and the Strong Parrott Theorem
%J Canadian mathematical bulletin
%D 2020
%P 813-824
%V 63
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000065/
%R 10.4153/S0008439520000065
%F 10_4153_S0008439520000065

Cité par Sources :