Extremal non-compactness of composition operators with linear fractional symbol

Abstract

We realize the norms of certain composition operators C φ with linear fractional symbol acting on the Hardy space in terms of the roots of associated hypergeometric functions. This realization leads to simple necessary and sufficient conditions on φ for C φ to exhibit extremal non-compactness, establishes equivalence of cohyponormality and cosubnormality of composition operators with linear fractional symbol, and yields a complete classification of those linear fractional φ that induce composition operators whose norms are determined by the action of the adjoint C φ ∗ on the normalized reproducing kernels in H 2 .