Geodesic
On the orthogonality of the white noise, given on a ring of operators, relatively to multiplicative shifts
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 3, pp. 640-644 
G. P. Bucan. On the orthogonality of the white noise, given on a ring of operators, relatively to multiplicative shifts. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 3, pp. 640-644. http://geodesic.mathdoc.fr/item/TVP_1976_21_3_a16/
@article{TVP_1976_21_3_a16,
     author = {G. P. Bucan},
     title = {On the orthogonality of the white noise, given on a ring of operators, relatively to multiplicative shifts},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {640--644},
     year = {1976},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_3_a16/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The article deals with a generalized Gaussian measure on the ring of all Hilbert–Shmidt operators $G_H$ on some separable Hilbert space $H$ with the characteristic functional $$ \varphi(z)=\exp\biggl\{-\frac{1}{2}\langle z,z\rangle\biggr\},\ \text{where}\ \forall u,v\in G_H\colon\langle u,v\rangle=\operatorname{Sp}uv^*. $$ Conditions are studied for $\mu\sim\mu u^{-1}$ where $u\in X_H$, the set of all linear operators on $H$, and $\mu u^{-1}(F)=\mu(u^{-1}F)=\mu(v\colon uv\in F)$ for those Borel sets $F$ on $G_H$ for which this equality makes sense.