Geodesic
Generalized Fredholm property and a priori estimates for linear operators on tensor products of Hilbert spaces
Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 902-912

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For a linear operator acting in a Hilbert space, the generalized Fredholm property (invertibility modulo a certain ideal) is proved to be equivalent to certain apriori estimates. This result is applied to establish a connection between properties of linear operators on tensor products of Hilbert spaces, such as $n$- and $d$-normality, the (generalized and ordinary) Fredholm property, and appropriate apriori estimates. 
@article{MZM_1998_64_6_a10,
     author = {V. S. Pilidi},
     title = {Generalized {Fredholm} property and a priori estimates for linear operators on tensor products of {Hilbert} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {902--912},
     publisher = {mathdoc},
     volume = {64},
     number = {6},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a10/}
}
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V. S. Pilidi. Generalized Fredholm property and a priori estimates for linear operators on tensor products of Hilbert spaces. Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 902-912. http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a10/