خاصيت بوخنر⁃ابرلين⁃داسبراي مدول ها و جبرهاي باناخ جابجايي

The Bochner-Eberlein-Doss property for modules an‎d commutative Banach algebras

رياضي محض

The main aim of this thesis is to investigate the BED property for some commuta-tive an‎d semisimple Banach algebras an‎d also commutative Banach modules. First, we introduce an‎d investigate the new concept of the BED Banach module. As the main results, we show that every BED algebra is a BED Banach module over itself. We also prove that every kernel ideal of a commutative C*-algebra is a BED Banach module on that commutative C*-algebra. Next, we investigate an‎d study the BED property for the closed ideals an‎d quotient algebras of any BED algebra. In fact, we prove that if A is a BED algebra, then all essential kernel ideals of A with closed character space are BED algebras. Furthermore, we show that if I is a kernel ideal of A an‎d _A is discrete an‎d b = CBSE(_A) then we always have (A ) = CBSE(_A ); In particular, A is a BED algebra. A III Then, assuming that A an‎d B aretwo commutative, semisimple, an‎d non-unital Banach d algebras an‎d θ ∈ _B, we investigate the BED property for their θ-Lau product, i.e. A×θ B, an‎d as a main result, we prove that A ×θ B is a BED algebra if an‎d only if Ae an‎d B are BED algebras. Finally, assuming that X is a locally compact an‎d Hausdorff space an‎d A is a commutative an‎d semisimple Banach algebra, we investigate the BED property for C0(X , A) an‎d show if C0(X , A) is a BED algebra then A is also a BED algebra. We also prove that the converse of this statement holds, for the case where X is discrete.

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