Linear Fractional Maps That Induce Compact Linear Operators

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Zakieldeen Aboabuda Mohammed Alhassn Ali, Sara Mustafa Alshareef Gesmallh, Amna Mahmoud Ahmed Bakhit, Manal Yagoub Ahmed Juma, Isra Abdalhleem Hassan Ali, Arafa .A.Alrhim Ahmed Dawood


It is generally known that the difference of two composition operators formed by linear fractional self-maps of a ball cannot be nontrivially compactly contained in the Hardy space or any common weighted Bergman space. This study extends this finding in two important ways: Inducing maps are expanded to linear fractional maps that carry a ball into a second, and the difference is extended to generic linear combinations, potentially higher-dimensional space.

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