Geodesic
Decomposition of Finite Schmidt Rank Bounded Operators on the Tensor Product of Separable Hilbert Spaces
Abdelkrim Bourouihiya1 ; Abdelkrim Bourouihiya
1Department of Mathematics, Nova Southeastern University, 3301 College Avenue, Fort Lauderdale, Florida
Acta mathematica Universitatis Comenianae, Tome 87 (2018) no. 1, pp. 15-24 
Abdelkrim Bourouihiya; Abdelkrim Bourouihiya. Decomposition of Finite Schmidt Rank Bounded Operators on the Tensor Product of Separable Hilbert Spaces. Acta mathematica Universitatis Comenianae, Tome 87 (2018) no. 1, pp. 15-24. http://geodesic.mathdoc.fr/item/AMUC_2018_87_1_a1/
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     title = { Decomposition of {Finite} {Schmidt} {Rank} {Bounded} {Operators} on the {Tensor} {Product} of {Separable} {Hilbert} {Spaces}},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {15--24},
     year = {2018},
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Inverse formulas for the tensor product are used to develop an algorithm to compute Schmidt decompositions of Finite Schmidt Rank (FSR) bounded operators on the tensor product of separable Hilbert spaces. The algorithm is then applied to solve inverse problems related to the tensor product of bounded operators. In particular, we show how properties of a FSR bounded operator are rejected by the operators involved in its Schmidt decomposition. These properties include compactness of FSR bounded operators and convergence of sequences whose terms are FSR bounded operators.