Geodesic
On Imprimitivity Hilbert Bimodules Over Commutative $H^*$-Algebras
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 451 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper, we introduce the notion of imprimitivity Hilbert $H^*$-bimodule and describe some properties of it. Moreover, we show that if $\mathcal{A}$ and $\mathcal{B}$ are proper and commutative $H^*$-algebras, $_\mathcal{A}E_\mathcal{B}$ is a Hilbert $H^*$-bimodule and $e_1$ is a minimal projection in $\mathcal{A}$ with $_\mathcal{A}[x|x]=e_1$ for some $x\in \mathcal{A}$, then $[x|x]_\mathcal{B}$ is a minimal projection in $\mathcal{B}$, too. Furthermore, the existence of orthonormal bases for such spaces is studied.
Classification : 46H05 46C05
Keywords: $\mathcal A$-$\mathcal B$-bimodule, $H^*$-algebra, full Hilbert $H^*$-module, minimal projection 
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     author = {M. Khanehgir and M. Moradian Khibary and Z. Niazi Moghani},
     title = {On {Imprimitivity} {Hilbert} {Bimodules} {Over} {Commutative} $H^*${-Algebras}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {451 },
     publisher = {mathdoc},
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     year = {2019},
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M. Khanehgir; M. Moradian Khibary; Z. Niazi Moghani. On Imprimitivity Hilbert Bimodules Over Commutative $H^*$-Algebras. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 451 . http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a8/