Resumen de Composition and translation operators on certain subspaces of the space of entire functions of bounded type
Manjul Gupta, Deepika Baweja
In this paper, for complex Banach spaces E, F and 1≤?≤∞ , the subspaces ??(?,?) of the space ?(?,?) consisting of holomorphic mappings of bounded type from E into F, have been introduced and studied. Here the notation ? stands for a comparison function ? which is an entire function defined on the complex plane, as ?(?)=∑∞?=0????,??>0 for each ?∈ℕ0 with ?1??→0 and ??+1??↓0 as n increases to ∞ . Besides considering the relationships amongst these spaces, their vector valued sequential analogues have also been obtained for 1≤?<∞ . These results are used in obtaining the dual and Schauder decomposition of ??(?,?) , 1≤?<∞ . The continuity of differentiation and translation operator has been proved by restricting ? suitably and the spectrum of the differentiation operator ?? has been investigated. Finally, the continuity and compactness of the composition operator ?? , defined corresponding to a holomorphic function ? have been investigated.
