Geodesic
On weak convergence in an infinite tensor product of Hilbert spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 318-322 
I. M. Burban. On weak convergence in an infinite tensor product of Hilbert spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 318-322. http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a1/
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     author = {I. M. Burban},
     title = {On weak convergence in an infinite tensor product of {Hilbert} spaces},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {318--322},
     year = {1971},
     volume = {9},
     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Investigation has been made of weakly convergent operator seria in the non-complete infinite tensor product of Hilbert spaces. It is proved that in the case when the dense domain exists, on which the sequences of partial sums of positive operators converge weakly, the limit operator is essentially self-adjoint.

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