6533b86efe1ef96bd12cc665
RESEARCH PRODUCT
Convex and expansive liftings close to two-isometries and power bounded operators
Laurian SuciuWitold Majdaksubject
Numerical AnalysisPure mathematicsAlgebra and Number Theory010102 general mathematicsHilbert spaceContext (language use)010103 numerical & computational mathematicsSpace (mathematics)01 natural sciencessymbols.namesakeOperator (computer programming)Bounded functionIsometrysymbolsDiscrete Mathematics and CombinatoricsGeometry and Topology0101 mathematicsInvariant (mathematics)Contraction (operator theory)Mathematicsdescription
Abstract In the context of Hilbert space operators, there is a strong relationship between convex and expansive operators and 2-isometries. In this paper, we investigate the bounded linear operators T on a Hilbert space H which have a 2-isometric lifting S on a Hilbert space K containing H as a closed subspace invariant for S ⁎ S . This last property holds in particular when S | K ⊖ H is an isometry. We relate such 2-isometric liftings S by some convex, concave or expansive liftings of the same type as S. We also examine some power bounded operators with such liftings, as well as an intermediate expansive lifting associated with T on the space H ⊕ l + 2 ( H ) . The latter notion is used to obtain 2-isometric liftings S for T (as above) and to describe the similarity of a quasi-expansive operator to a contraction.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-05-01 | Linear Algebra and its Applications |