An investigation of approximately biprojective Banach algebras

Subject Areas : Statistics

Mohammad Hossein  Sattari ¹ (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751- 71379, Iran)

Received: 2019-11-12 Accepted : 2020-09-21 Published : 2021-07-23

Keywords: عملگر قطری, دوگان دوم جبر باناخ, ضرب آرنز, جبر های باناخ ادغامی,

Abstract :

The concept of approximately biprojective Banach algebras has been introduced by Pourmahmood-Aghababa [15], O. Ya. Aristov [2] and Y. Zhang [19] in different aspects of approximation. Here we follow the definition provided by Pourmahmood-Aghababa that is more general with an abundant amount of various interesting examples, and less restrictive conditions. In this paper, some hereditary properties of this notion are investigated. Indeed, we show that approximate biprojectivity of the second dual of a Banach algebra A (equipped with Arens product) implies approximate biprojectivity of A. This concept is also investigated on amalgamated Banach algebras that are genuine generalization of the direct sum of Banach algebras and includes the unitization, the Lau product, the semidirect product, and the module extension Banach algebras. We prove that the first summand in an approximately biprojective amalgamated Banach algebra is approximately biprojective, while for approximate biprojectivity of the second summand some additional hypothesis are necessary.

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