Every weakly compact composition operator between weighted Banach spaces $H_v^{\infty}$ of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space $H_v^{\infty}$ are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

Keywords:

weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operator weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operator

MSC Classifications:

47B38, 30D55, 46E15 show english descriptions Operators on function spaces (general)
${H}^p$-classes
Banach spaces of continuous, differentiable or analytic functions 47B38 - Operators on function spaces (general)
30D55 - ${H}^p$-classes
46E15 - Banach spaces of continuous, differentiable or analytic functions

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