Generalized Fredholm property and a priori estimates for linear operators on tensor products of Hilbert spaces

For a linear operator acting in a Hilbert space, the generalized Fredholm property (invertibility modulo a certain ideal) is proved to be equivalent to certaina priori estimates. This result is applied to establish a connection between properties of linear operators on tensor products of Hilbert spaces, such asn- andd-normality, the (generalized and ordinary) Fredholm property, and appropriatea priori estimates.Translated fromMatematicheskie Zametki, Vol. 64, No. 6, pp. 902–912, December, 1998.The author is grateful to V. M. Deundyak for useful discussion of this work.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01195.