id: 06110319
dt: j
an: 06110319
au: Allen, Robert F.; Colonna, Flavia; Easley, Glenn R.
ti: Multiplication operators on the iterated logarithmic Lipschitz spaces of a
    tree.
so: Mediterr. J. Math. 9, No. 4, 575-600 (2012).
py: 2012
pu: Birkhäuser (Springer), Basel
la: EN
cc: 
ut: multiplication operators; trees; Lipschitz space
ci: 
li: doi:10.1007/s00009-011-0157-1
ab: Summary: We introduce a class of iterated logarithmic Lipschitz spaces
    $\mathcal{L}^{(k)}, k \in \mathbb{N}$, on an infinite tree which arise
    naturally in the context of operator theory. We characterize
    boundedness and compactness of the multiplication operators on
    ${\mathcal{L}^{(k)}}$ and provide estimates on their operator norm and
    their essential norm. In addition, we determine the spectrum,
    characterize the multiplication operators that are bounded below, and
    prove that on such spaces there are no nontrivial isometric
    multiplication operators and no isometric zero divisors.
rv: