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Published 1996 | public
Journal Article

The unique extremal QC mapping and uniqueness of Hahn-Banach extensions

Abstract

Let χ be an essentialy bounded complex valued measurable function defined on the unit disc Δ, and let Λ_χ be the corresponding linear functional on the space B of analytic L^1-integrable functions. An outline of proof of main steps of the following is given: If |χ| is a constant function in Δ, then the uniqueness of Hahn-Banach extension of Λ_χ, from B to L^1, when ||Λ_ χ|| = ||χ||∞, implies that χ is the unique complex dilatation. We give a short review of some related results.

Additional Information

© 1996 European Mathematical Society. Received 04.11.1996. Supported by Ministry of Science and technology RS, grant number 04M01.

Additional details

Created:
August 20, 2023
Modified:
October 25, 2023