6533b85bfe1ef96bd12ba90c

RESEARCH PRODUCT

Partial isometries and the conjecture of C.K. Fong and S.K. Tsui

Laurian SuciuMostafa Mbekhta

subject

Partial isometryConjectureApplied Mathematics010102 general mathematicsInvariant subspaceHilbert space010103 numerical & computational mathematics01 natural sciencesCombinatoricssymbols.namesakeNilpotent operatorQuasi-isometryBounded functionsymbolsMathematics::Metric Geometry0101 mathematicsContraction (operator theory)AnalysisMathematics

description

Abstract We investigate some bounded linear operators T on a Hilbert space which satisfy the condition | T | ≤ | Re T | . We describe the maximum invariant subspace for a contraction T on which T is a partial isometry to obtain that, in certain cases, the above condition ensures that T is self-adjoint. In other words we show that the Fong–Tsui conjecture holds for partial isometries, contractive quasi-isometries, or 2-quasi-isometries, and Brownian isometries of positive covariance, or even for a more general class of operators.

yearjournalcountryeditionlanguage
2016-05-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2015.12.057