Geodesic
On weak convergence in an infinite tensor product of Hilbert spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 318-322

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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. 
@article{TMF_1971_9_3_a1,
     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},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a1/}
}
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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/