Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

C*-algebraic Bieberbach, Robertson, Lebedev-Milin, Zalcman, Krzyz and Corona Conjectures

Version 1 : Received: 28 July 2022 / Approved: 8 August 2022 / Online: 8 August 2022 (09:53:02 CEST)

How to cite: KRISHNA, K.M. C*-algebraic Bieberbach, Robertson, Lebedev-Milin, Zalcman, Krzyz and Corona Conjectures. Preprints 2022, 2022080140 (doi: 10.20944/preprints202208.0140.v1). KRISHNA, K.M. C*-algebraic Bieberbach, Robertson, Lebedev-Milin, Zalcman, Krzyz and Corona Conjectures. Preprints 2022, 2022080140 (doi: 10.20944/preprints202208.0140.v1).

Abstract

We study C*-algebraic versions of following conjectures/theorems: (1) Bieberbach conjecture (de Branges theorem) (2) Robertson conjecture (3) Lebedev-Milin conjecture (4) Zalcman conjecture (5) Krzyz conjecture (6) Corona conjecture (Carleson theorem). We prove that the C*-algebraic Bieberbach Conjecture for invertible coefficients is true for second degree C*-algebraic polynomials.

Keywords

C*-algebra; Bieberbach conjecture; de Branges theorem; Robertson conjecture; Lebedev-Milin conjecture; Zalcman conjecture; Krzyz conjecture; Corona conjecture; Riemann mapping theorem

Subject

MATHEMATICS & COMPUTER SCIENCE, Analysis

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