Rank one perturbations of 2-isometries

2025/08/13 by Nailwal, Rajkamal
#47B02 #47B38 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.09701

Abstract

In this paper, we investigate when a rank-one perturbation of a 2-isometry remains a 2-isometry. As an application, we identify several classes of 2-isometries on function spaces.

Citations

• Analyticity, rank one perturbations and the invariance of the left spectrum
• Left-invertibility of rank-one perturbations
• Invariant subspace problem for rank-one perturbations: the quantitative version
• Spectra of rank-one perturbations of self-adjoint operators
• A solution to the Cauchy dual subnormality problem for 2-isometries

Related

• Rank metric isometries and determinant-preserving mappings on II₁-factors
• On Quasinormality of compact perturbations of the isometries
• 2-local isometries on function spaces
• Left-invertibility of rank-one perturbations
• Cyclic Analytic 2-isometry of Finite Rank and Cauchy Dual Subnormality Problem