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Article
Open AccessOn the Structure of Conditionally Positive Definite Algebraic Operators
Recently, the authors have introduced and intensively studied a class of bounded Hilbert space operators called conditionally positive definite. Its origins go back to the harmonic analysis on
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Article
Open AccessTaylor spectrum approach to Brownian-type operators with quasinormal entry
In this paper, we introduce operators that are represented by upper triangular \(2\times 2\) ...
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Article
Open AccessA Subnormal Completion Problem for Weighted Shifts on Directed Trees, II
The subnormal completion problem on a directed tree is to determine, given a collection of weights on a subtree, whether the weights may be completed to the weights of a subnormal weighted shift on the directe...
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Article
A Subnormal Completion Problem for Weighted Shifts on Directed Trees
Given a directed tree and a collection of weights on a subtree, the subnormal completion problem is to determine whether the weights may be completed to the weights of an injective, bounded, subnormal weighted sh...
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Chapter
Preliminaries
The classical Banach-Stone theorem (see [7, Théorème XI.3] and [146], see also [68, Theorem 2.1.1]) states that if X and Y are compact Hausdorff topological spaces and A: C(X) → C(Y ) is a surjective linear iso...
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Chapter
Subnormality: General Criteria
The main goal of this chapter is to provide criteria for the subnormality of (not necessarily bounded) weighted composition operators. The first criterion, which is given in Sect. 3.1, requires that h ϕ,w > 0 a.e...
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Chapter
Seminormality
In this chapter, we give characterizations of seminormal, formally normal, symmetric, selfadjoint and positive selfadjoint weighted composition operators. Hyponormality and cohyponormality are characterized in...
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Chapter
Relationships Between Cϕ,w and C ϕ
In this chapter, we investigate the interplay between selected properties of a weighted composition operator C ϕ,w and the corresponding composition operator C ϕ . In Sect. 7.1, we discuss the questions of when ...
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Chapter
Preparatory Concepts
This chapter introduces some concepts of measure theory that will be useful for studying weighted composition operators (including the Radon-Nikodym derivative h ϕ,w and the conditional expectation ...
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Chapter
C ∞ -Vectors
In this chapter, we turn our interest to weighted composition operators that have sufficiently many
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Chapter
Discrete Measure Spaces
In this chapter, we adapt our general results to the context of discrete weighted composition operators, i.e., weighted composition operators over discrete measure spaces. Section 6.1 has an introductory chara...
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Chapter
Miscellanea
This chapter consists of three sections. In Section 8.1, we discuss the problem of whether the tensor product of (finitely many) weighted composition operators can be regarded as a weighted composition operato...
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Article
Semi-cubic Hyponormality of Weighted Shifts with Stampfli Recursive Tail
Let \(\alpha :\sqrt{x_{m}},\ldots ,\sqrt{x_{1}},(\sqrt{u},\sqrt{v},\sqrt{w} )^{\wedge }\) ...
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Article
On unbounded composition operators in \(L^2\) -spaces
Fundamental properties of unbounded composition operators in \(L^2\) -spaces are studied. Characterizations of normal ...
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Article
Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality
Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of...
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Article
Open AccessUnbounded Quasinormal Operators Revisited
Various characterizations of unbounded closed densely defined operators commuting with the spectral measures of their moduli are established. In particular, Kaufman’s definition of an unbounded quasinormal ope...
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Article
Normal Extensions Escape from the Class of Weighted Shifts on Directed Trees
A formally normal weighted shift on a directed tree is shown to be a bounded normal operator. The question of whether a normal extension of a subnormal weighted shift on a directed tree can be modeled as a wei...
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Article
On Semi-weakly n-Hyponormal Weighted Shifts
Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved...
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Article
Block Matrix Operators and Weak Hyponormalities
We introduce a new model of a block matrix operator M(α, β) induced by two sequences α and β and characterize its p-hyponormality. The model may be viewed as arising from the composition operator C ...
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Book and Conference Proceedings
