6533b7d9fe1ef96bd126bfc2
RESEARCH PRODUCT
Operators intertwining with isometries and Brownian parts of 2-isometries
Laurian SuciuMostafa MbekhtaWitold Majdaksubject
Numerical AnalysisPure mathematicsPartial isometryAlgebra and Number Theory010102 general mathematicsMathematical analysisInvariant subspaceHilbert space010103 numerical & computational mathematics01 natural sciencesUnitary statesymbols.namesakeQuasi-isometrysymbolsDiscrete Mathematics and CombinatoricsGeometry and Topology0101 mathematicsContraction (operator theory)Subspace topologyBrownian motionMathematicsdescription
Abstract For two operators A and T ( A ≥ 0 ) on a Hilbert space H satisfying T ⁎ A T = A and the A-regularity condition A T = A 1 / 2 T A 1 / 2 we study the subspace N ( A − A 2 ) in connection with N ( A T − T A ) , for T belonging to different classes. Our results generalize those due to C. Kubrusly concerning the case when T is a contraction and A = S T is the asymptotic limit of T. Also, the particular case of a 2-isometry in the sense of S. Richter as well as J. Agler and M. Stankus is considered. For such operators, under the same regularity condition we completely describe the reducing Brownian unitary and isometric parts, as well as the invariant Brownian isometric part. Some examples are provided in order to illustrate the limits of the theoretical results.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-11-01 | Linear Algebra and its Applications |