Geodesic
Complete Indefiniteness Tests for Jacobi Matrices with Matrix Entries
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 32-37

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We study the problem concerning the maximality of the deficiency indices of operators generated by symmetric Jacobi matrices with matrix entries in the space $l_2$. Effective conditions for the maximality of the deficiency indices are given in terms of entries of the Jacobi matrix. These conditions are new even in the scalar (one-dimensional) case. 
@article{FAA_2001_35_4_a4,
     author = {A. G. Kostyuchenko and K. A. Mirzoev},
     title = {Complete {Indefiniteness} {Tests} for {Jacobi} {Matrices} with {Matrix} {Entries}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {32--37},
     publisher = {mathdoc},
     volume = {35},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a4/}
}
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A. G. Kostyuchenko; K. A. Mirzoev. Complete Indefiniteness Tests for Jacobi Matrices with Matrix Entries. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 4, pp. 32-37. http://geodesic.mathdoc.fr/item/FAA_2001_35_4_a4/