Spectral radius of weighted composition operators in $L^{p}$-spaces

• Autorzy: Krzysztof Zajkowski
• Języki publikacji: EN

Abstrakty

EN

We prove that for the spectral radius of a weighted composition operator $aT_{α}$, acting in the space $L^{p}(X,𝓑,μ)$, the following variational principle holds:
$ln r (aT_{α}) = max_{ν ∈ M¹_{α,e}} ∫_{X} ln|a|dν$,
where X is a Hausdorff compact space, α: X → X is a continuous mapping preserving a Borel measure μ with suppμ = X, $M¹_{α,e}$ is the set of all α-invariant ergodic probability measures on X, and a: X → ℝ is a continuous and $𝓑_{∞}$-measurable function, where $𝓑_{∞}= ⋂_{n=0}^{∞} α^{-n}(𝓑)$. This considerably extends the range of validity of the above formula, which was previously known in the case when α is a homeomorphism.

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 44A15: Special transforms (Legendre, Hilbert, etc.)
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 3
• Strony: 301-307

Daty

wydano

2010

Twórcy

autor

Krzysztof Zajkowski

• Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland

Identyfikatory

DOI

10.4064/sm198-3-8