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

Krzysztof Zajkowski. "Spectral radius of weighted composition operators in $L^{p}$-spaces." Studia Mathematica 198.3 (2010): 301-307. <http://eudml.org/doc/285428>.

@article{KrzysztofZajkowski2010,
abstract = {We prove that for the spectral radius of a weighted composition operator $aT_\{α\}$, acting in the space $L^\{p\}(X,,μ)$, 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 $_\{∞\}$-measurable function, where $_\{∞\}= ⋂_\{n=0\}^\{∞\} α^\{-n\}()$. This considerably extends the range of validity of the above formula, which was previously known in the case when α is a homeomorphism.},
author = {Krzysztof Zajkowski},
journal = {Studia Mathematica},
language = {eng},
number = {3},
pages = {301-307},
title = {Spectral radius of weighted composition operators in $L^\{p\}$-spaces},
url = {http://eudml.org/doc/285428},
volume = {198},
year = {2010},
}

TY - JOUR
AU - Krzysztof Zajkowski
TI - Spectral radius of weighted composition operators in $L^{p}$-spaces
JO - Studia Mathematica
PY - 2010
VL - 198
IS - 3
SP - 301
EP - 307
AB - We prove that for the spectral radius of a weighted composition operator $aT_{α}$, acting in the space $L^{p}(X,,μ)$, 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 $_{∞}$-measurable function, where $_{∞}= ⋂_{n=0}^{∞} α^{-n}()$. This considerably extends the range of validity of the above formula, which was previously known in the case when α is a homeomorphism.
LA - eng
UR - http://eudml.org/doc/285428
ER -