Left inverses of matrices with polynomial decay
Copyright policy )Left inverses of matrices with polynomial decay
The algebra of Schur operators on l^2 is known not to be inverse-closed. When l^2=l^2(X) where X is a metric space, we can consider elements of the Schur algebra with certain decay at infinity. For instance if X has the doubling property, then Q. Sun has proved that the weighted Schur algebra for a strictly polynomial weight is inverse-closed. Here, we prove a result dealing with left-invertibility. Namely, if such an operator is bounded below in l^p for some p, then it is bounded below for all q, and it admits a left-inverse in the weighted Schur algebra.
24 pages
- Vanderbilt University United States
- École Normale Supérieure de Lyon France
General (adjoints, conjugates, products, inverses, domains, ranges, etc.), Basic linear algebra, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, stability of Schur operators, Stability of Schur operators, left inverse for infinite matrices with off-diagonal decay, Left inverse for infinite matrices with off-diagonal decay, 47B38, 47B37, FOS: Mathematics, Analysis
General (adjoints, conjugates, products, inverses, domains, ranges, etc.), Basic linear algebra, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, stability of Schur operators, Stability of Schur operators, left inverse for infinite matrices with off-diagonal decay, Left inverse for infinite matrices with off-diagonal decay, 47B38, 47B37, FOS: Mathematics, Analysis
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