Extreme positive operators on $C(X)$ which commute with given operators

On Extreme Averaging Operators

Hypercyclic Operators That Commute with the Bergman Backward Shift

The backward shift B on the Bergman space of the unit disc is known to be hypercyclic (meaning: it has a dense orbit). Here we ask: “Which operators that commute with B inherit its hypercyclicity?” We show that the problem reduces to the study of operators of the form φ(B) where φ is a holomorphic self-map of the unit disc that multiplies the Dirichlet space into itself, and that the question o...

Composition Operators and Multiplication Operators on Orlicz Spaces

This article has no abstract.

On Composition Operators Which Preserve Bmo

Q |f − fQ|dx < ∞, (1) where |Q| is the n-dimensional Lebesgue measure of Q, fQ = |Q|−1 ∫ Q fdx, and the supremum is taken over all closed cubes Q ⊂ D with sides parallel to the coordinate axes. Let D and D′ be subdomains of Rm and Rn, m, n ≥ 1, respectively. We say that a map F : D → D′ is measurable if F−1(E) is measurable for each measurable subset E of D′. We say that a measurable map F : D ...

Products of Positive Operators

A number of mathematicians have considered the problem of writing an operator as a product of \nice" operators, such as positive, hermitian or normal operators. Our principal reference for this is a paper of P.Y. Wu 6], but see also 2] and 5]. This kind of question, and related questions, have also been considered in a C*-algebra context, see 3]. A core result of Wu's paper is his theorem that ...