Multiplication Operators on the Iterated Logarithmic Lipschitz Spaces of a Tree

Allen, Robert F.; Colonna, Flavia; Easley, Glenn R.

doi:10.1007/s00009-011-0157-1

Cited by 24 publications

(19 citation statements)

References 9 publications

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“…In particular, infinite trees can be seen as the natural discretizations of the hyperbolic disk. Much more information about these topics can be found in the papers [1,2,3,4,9,10,11,19]. We should mention that the paper [19] studies hypercyclicity for composition operators defined on the boundary of nondirected trees.…”

Section: Introductionmentioning

confidence: 99%

Hypercyclicity of shifts on weighted L spaces of directed trees

Martínez-Avendaño

2017

Journal of Mathematical Analysis and Applications

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In this paper, we study the hypercyclicity of forward and backward shifts on weighted L p spaces of a directed tree. In the forward case, only the trivial trees may support hypercyclic shifts, in which case the classical results of Salas [21] apply. For the backward case, nontrivial trees may support hypercyclic shifts. We obtain necessary conditions and sufficient conditions for hypercyclicity of the backward shift and, in the case of a rooted tree on an unweighted space, we show that these conditions coincide.

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Section: Introductionmentioning

confidence: 99%

Hypercyclicity of shifts on weighted L spaces of directed trees

Martínez-Avendaño

2017

Journal of Mathematical Analysis and Applications

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“…Colonna multiplication operators on Lipschitz space, weighted Lipschitz space, and iterated logarithmic Lipschitz space of a tree in [10], [4] and [3], respectively. In [2,11], the authors discussed about multiplication operators between Lipschitz type spaces and the space of bounded functions on a tree.…”

Section: Introductionmentioning

confidence: 99%

Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees

Muthukumar¹,

Ponnusamy²

2016

Anal.Math.Phys.

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Abstract. In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability, growth estimate for functions in these spaces and their consequences. Equivalent conditions for multiplication operators to be bounded and compact are also obtained. Furthermore, we discuss about point spectrum, approximate point spectrum and spectrum of multiplication operators and discuss when a multiplication operator is an isometry.

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“…Therefore, the number of vertices in D n 1 which are mapped into D k is strictly less than c k N k,n 1 . Then by (2), the total number of elements in D n 1 is strictly less than…”

Section: Isometrymentioning

confidence: 99%

“…The basic questions such as boundedness, compactness, estimates for operator norm and essential norm, isometry and spectrum were considered for multiplication operators between various discrete function spaces on infinite tree such as Lipschitz space, weighted Lipschitz space and iterated logarithmic Lipschitz spaces. See [1,2,3,5,9,10] for more details.…”

Section: Introductionmentioning

confidence: 99%

Composition operators on Hardy spaces of the homogenous rooted trees

Muthukumar

Ponnusamy

2020

Monatsh Math

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In [16], the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space T p defined on a homogeneous rooted tree. In this article, we give equivalent conditions for the composition operator C φ to be bounded on T p and on T p,0 spaces and compute their operator norm. We also characterize invertible composition operators as well as isometric composition operators on T p and on T p,0 spaces. Also, we discuss the compactness of C φ on T p and finally prove there are no compact composition operators on T p,0 spaces.2000 Mathematics Subject Classification. Primary: 05C05, 37E25, 47B33, 47B38; Secondary: 30H10, 46B50.

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Multiplication Operators on the Iterated Logarithmic Lipschitz Spaces of a Tree

Cited by 24 publications

References 9 publications

Hypercyclicity of shifts on weighted L spaces of directed trees

Hypercyclicity of shifts on weighted L spaces of directed trees

Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees

Composition operators on Hardy spaces of the homogenous rooted trees

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