Geodesic
Algebraic Distance Between Submodules
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 44 (2019) no. 1 
Dragan S. Djordjević. Algebraic Distance Between Submodules. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 44 (2019) no. 1. http://geodesic.mathdoc.fr/item/BASS_2019_44_1_a4/
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     author = {Dragan S. Djordjevi\'c},
     title = {Algebraic {Distance} {Between} {Submodules}},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {75 - 89},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/BASS_2019_44_1_a4/}
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We investigate the algebraic distance between closed and orthogonaly complemented submodules of a Hilbert $C^*$-module, which is defined as the norm of a difference of corresponding orthogonal projections. Some results are proved using $2\times2$ decompositions of adjointable operators.