Spectra of Weighted Composition Operators on Analytic Function Spaces

Abstract

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Exact essential norm of generalized Hilbert matrix operators on classical analytic function spaces

“…To obtain the essential norm we first consider the space A p α . By combining the following standard approach (see Proposition 3.6 in [12])…”

Invertible and Isometric Weighted Composition Operators

“…The earliest explicit references on WCOs are [28] and [29]. There is a large body of work on the subject: [3][4][5]8,[13][14][15]21,23,31,33,34], to mention only some more recent references on the boundedness, compactness, or questions related to the spectra of such operators.…”

Spectral properties of weighted composition operators on $\Hol(\D)$ induced by rotations

“…In these two books as well as in the vast literature on this subject, these operators are considered on Banach spaces of analytic functions such as the disc algebra A(D) or the Hardy spaces H p (D). More generally, one may multiply by a weight and consider weighted composition operators as in the classical article [10] by Kamowitz or more recent contributions by Bourdon [4], Bonet et al [3], Chalendar et al [5], Galindo et al [8], Hyvärinen et al [9].…”