Ruhan Zhao

Topological structure of the space of composition operators onH

Components and isolated points of the topological space of composition operators onH∞ in the uniform operator topology are characterized. Compact differences of two composition operators are also characterized. With the aid of these results, we show that a component inC(H∞) is not in general the set of all composition operators that differ from the given one by a compact operator.

Weighted Composition Operators on the Bergman Space

Bounded, compact and Schatten class weighted composition operators on the Bergman space are characterized by the use of generalized Berezin transforms. An estimate of the essential norms of weighted composition operators on the Bergman space is given. Most of the results remain true for Hardy spaces and weighted Bergman spaces.

Weighted composition operators on the Bloch space

f = uf o ip.It is easy to see that an operator defined in this manner is linear. We can regard thisoperator as a generalisation of a multiplication operator and a composition operator.In this note we study the boundedness and the compactness of weighted compositionoperators on the Bloch space and the little Bloch space. Recall that a function /analytic in D is said to belong to the Bloch space B ifsup(l-|z|

Generalized Schwarz-Pick estimates

We obtain higher derivative generalizations of the Schwarz-Pick inequality for analytic self-maps of the unit disk as a consequence of recent characterizations of boundedness and compactness of weighted composition operators between Bloch-type spaces.

Schwarz–Pick Type Estimates

We obtain estimates on higher-order derivatives that generalize the classical Schwarz–Pick inequality for analytic self-maps of the unit disk. We discuss further extensions involving certain weight functions, converse results, and versions of all of these results in the setting of the unit ball in .

Toeplitz operators on Bloch-type spaces

We characterize complex measures μ on the unit disk for which the Toeplitz operator T α μ , a > 0, is bounded or compact on the Bloch type spaces B α .

Essential norm estimates of weighted composition operators between Bergman spaces on strongly pseudoconvex domains

We give estimates of the essential norms of weighted composition operators acting between Bergman spaces on strongly pseudoconvex domains. We also characterize boundedness and compactness of these operators.