Decomposition of Finite Schmidt Rank Bounded Operators on the Tensor Product of Separable Hilbert Spaces

Authors

Abdelkrim Bourouihiya, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

2016

Publication Title

Acta Mathematica Universitatis Comenianae

Keywords

Hilbert spaces, Tensor product of operators, Schmidt decomposition, Compact operators, Inverse problems

ISSN

0862-9544

First Page

1

Last Page

10

Abstract

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 reflected 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.

NSUWorks Citation

Bourouihiya, Abdelkrim, "Decomposition of Finite Schmidt Rank Bounded Operators on the Tensor Product of Separable Hilbert Spaces" (2016). Mathematics Faculty Articles. 209.
https://nsuworks.nova.edu/math_facarticles/209

ORCID ID

0000-0002-5456-7745