In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined an infinite rooted tree. We discuss, through its connection with composition operators, boundedness and compactness operator. addition, discuss norm spectrum, consider when such can be isometry. then apply these results to Lipschitz space weighted Banach spaces, as well H...

The boundedness of the difference of two weighted composition operators from weighted Bergman spaces to weighted-type spaces in the unit ball are investigated in this paper.

In this paper, we characterize those holomorphic symbols u on the unit ball B and holomorphic self-mappings φ of B for which the weighted composition operator uCφ is bounded or compact from Bloch-type space to H∞ space. Mathematics subject classification (2010): Primary 47B33; Secondary 47B38.

Let φ be an analytic self-map of the open unit polydisk D , N ∈ N. Such a map induces a composition operator Cφ acting on weighted Banach spaces of holomorphic functions. We study when such operators are power bounded resp. uniformly mean ergodic. Mathematics Subject Classification (2010): 47B33, 47B38

By using generalized Salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. Coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.

Suppose X and Y are locally compact Hausdorff spaces, E and F are Banach spaces and F is strictly convex. We show that every linear isometry T from C0(X, E) into C0(Y, F) is essentially a weighted composition operator T f (y) = h(y)(f (ϕ(y))).

Let φ be a holomorphic self-map of the open unit ball B, g ∈ H(B). In this paper, the boundedness and compactness of the Volterra composition operator T g from generally weighted Bloch spaces to Bloch-type spaces are investigated. c ©2012 NGA. All rights reserved.

Let φ be a holomorphic self-map of the open unit polydisk U in C and p, q > 0. In this paper, the generally weighted Bloch spaces B log(U ) are introduced, and the boundedness and compactness of composition operator Cφ from B p log(U ) to B log(U ) are investigated.