Geodesic
The triangle equality in Hilbert $A$-modules
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 38-45

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We show that for any two elements $x$, $y$ of Hilbert $A$-module $M$ over local $C^*$-algebra $A$ the generalized triangle equality $|x+y|=|x|+|y|$ holds if and only if $\langle x,y\rangle=|x||y|$.
Keywords: local $C^{\ast}$-algebra, Hilbert $A$-module, local Hilbert space, module compact operator, triangle equality.
Mots-clés : $\ast$-homomorphism 
@article{IVM_2019_10_a4,
     author = {A. V. Kalinichenko and M. A. Pliev},
     title = {The triangle equality in {Hilbert} $A$-modules},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {38--45},
     publisher = {mathdoc},
     number = {10},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_10_a4/}
}
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A. V. Kalinichenko; M. A. Pliev. The triangle equality in Hilbert $A$-modules. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2019), pp. 38-45. http://geodesic.mathdoc.fr/item/IVM_2019_10_a4/