Sectorial operators on Wiener algebras of analytic functions (Q968883)

The Wiener algebra of absolutely convergent Taylor series of a complex variable \[ x(\xi)=\sum_{n\in\mathbb{N}}c_{n}\xi^{n}\text{ with }\left\| x\right\| _{W}=\sum_{n\in\mathbb{N}}\left| c_{n}\right| <\infty \] was extended to the infinite-dimensional setting for Hilbert spaces in [\textit{O.\,V.\thinspace Lopushansky} and \textit{A.\,V.\thinspace Zagorodnyuk}, Ann.\ Pol.\ Math.\ 81, No.\,2, 111--122 (2003; Zbl 1036.46030)] by using Hilbert-Schmidt polynomials instead of power summands \(c_{n}\xi^{n}\). In the present paper, the author investigates a Banach infinite-dimensional generalization, called approximation Wiener algebras, where approximable polynomials are used as the power summads in the Taylor series, instead of Hilbert-Schmidt polynomials. As the title of the paper indicates, the author investigates quantized sectorial operators acting on approximable Wiener type algebras of analytic functions. For such operators, a sufficient condition of a sectorial property is established and a holomorphic calculus is constructed.