Linear isometries on the annulus: description and spectral properties
Copyright policy )Linear isometries on the annulus: description and spectral properties
We give a complete characterisation of the linear isometries of ${\rm Hol}(Ω)$, where $Ω$ is the half-plane, the complex plane or an annulus centered at 0 and symmetric to the unit circle. Moreover, we introduce new techniques to describe the holomorphic maps on the annulus that preserve the unit circle, and we finish by proving results about the spectra of the linear isometries on the annulus.
15 pages
- Panthéon-Assas University France
- University of Paris France
- UNIVERSITE GUSTAVE EIFFEL France
- Paris-East Créteil University France
- University of Leeds United Kingdom
Mathematics - Complex Variables, 47B33, 30H05, 47A10, annulus, Linear composition operators, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], spectrum, Functional Analysis (math.FA), Mathematics - Functional Analysis, weighted composition operator, isometry, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], holomorphic functions, FOS: Mathematics, Spaces of bounded analytic functions of one complex variable, Fréchet space, Spectrum, resolvent, Complex Variables (math.CV)
Mathematics - Complex Variables, 47B33, 30H05, 47A10, annulus, Linear composition operators, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], spectrum, Functional Analysis (math.FA), Mathematics - Functional Analysis, weighted composition operator, isometry, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], holomorphic functions, FOS: Mathematics, Spaces of bounded analytic functions of one complex variable, Fréchet space, Spectrum, resolvent, Complex Variables (math.CV)
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