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

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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 
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/
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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 },
     year = {2019},
     volume = {43},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a8/}
}
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