Extremal non-compactness of composition operators with linear fractional symbol. (English) Zbl 1108.47024

The norm of certain composition operators with linear fractional symbol acting on the Hardy space in terms of the roots of associated hypergeometric functions is realized in this paper. The realization leads to simple necessary and sufficient conditions on \(\phi\) for the composition operator 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 symbols that induce composition operators whose norms are determined by the action of the adjoint of the composition operator on the normalized reproducing kernels in Hardy space.


47B33 Linear composition operators
47B38 Linear operators on function spaces (general)
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