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June 2020 On the Banach algebra structure for C(n) of the bidisc and related topics
Ramiz Tapdıgoglu
Illinois J. Math. 64(2): 185-197 (June 2020). DOI: 10.1215/00192082-8303477

Abstract

Let C(n)=C(n)(D×D) be a Banach space of complex valued functions f(x,y) that are continuous on the closed bidisc D×D¯, where D={zC:|z|<1} is the unit disc in the complex plane C and has nth partial derivatives in D×D which can be extended to functions continuous on D×D¯. The Duhamel product is defined on C(n) by the formula (fg)(z,w)=2zw0z0wf(zu,wv)g(u,v)dvdu. In the present paper we prove that C(n)(D×D) is a Banach algebra with respect to the Duhamel product . This result extends some known results. We also investigate the structure of the set of all extended eigenvalues and extended eigenvectors of some double integration operator Wzw. In particular, the commutant of the double integration operator Wzw is also described.

Citation

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Ramiz Tapdıgoglu. "On the Banach algebra structure for C(n) of the bidisc and related topics." Illinois J. Math. 64 (2) 185 - 197, June 2020. https://doi.org/10.1215/00192082-8303477

Information

Received: 15 September 2019; Revised: 5 December 2019; Published: June 2020
First available in Project Euclid: 1 May 2020

zbMATH: 07210956
MathSciNet: MR4092955
Digital Object Identifier: 10.1215/00192082-8303477

Subjects:
Primary: 46E35
Secondary: 47B38, 47B47

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 2 • June 2020
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