Details

Autor(en) / Beteiligte

• Colonna, Flavia
• Martínez-Avendaño, Rubén A.

Titel

Some classes of operators with symbol on the Lipschitz space of a tree

Ist Teil von

• Mediterranean journal of mathematics, 2017-02, Vol.14 (1), p.1-25, Article 18

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2017

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we expand the study of the multiplication operators on the Lipschitz space of a tree begun in Colonna and Easley (Integral Equ Oper Theory 68:391–411, 2010 ) by focusing on their adjoint acting on a certain separable subspace of the Lipschitz space whose dual is isometrically isomorphic to L 1 . We then study the properties of two useful operators ∇ and Δ and use them (along with the multiplicative symbol ψ ) to define the Toeplitz operator T ψ on the space L p for 1 ≤ p ≤ ∞ . We give conditions for its boundedness and study its point spectrum.