List of Articles Lau product

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  1 - Derivations on Lau product of Banach algebras
  Saeid Shams
  Extension of Banach algebras defined by Cartesian product by a linear functional such as are called -Lau Banach algebras. Recently, this type of Banach algebras are interested by many researchers. Derivations play an important role in algebraic structures. By using this More

  Extension of Banach algebras defined by Cartesian product by a linear functional such as are called -Lau Banach algebras. Recently, this type of Banach algebras are interested by many researchers. Derivations play an important role in algebraic structures. By using this role, one can discover some of the properties of algebraic structures on which a derivation is defined, such as their semi simplicity. In this paper, we consider derivations that are defined on Lau product of Banach algebras and we characterize these derivations in some various cases. As a main characterization, for two Banach algebra , and , we show that is a derivation if and only if there are derivations , and a -derivation such that for all . We investigate the converse case of the above obtained result in some various cases and according to the obtained results related to characterization of derivations, we investigate and characterize the first cohomology of Banach algebras obtained by this product. Manuscript profile
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  2 - Characterization of cubic derivations on various class of Banach algebras
  Fariba Farajpour Ali Ebadian Shahram Najafzadeh
  Let A be a Banach algebra and X be a Banach A-bimodule. A mapping D:A--->X is called a cubic derivation if, for all a,bin A we have D(ab)=a^3D(b)+D(a)b^3 . The mapping D:A--->X is called a cubic homogenous map if we have D(lambda a)=lambda^3 D(a) for all ain A and More

  Let A be a Banach algebra and X be a Banach A-bimodule. A mapping D:A--->X is called a cubic derivation if, for all a,bin A we have D(ab)=a^3D(b)+D(a)b^3 . The mapping D:A--->X is called a cubic homogenous map if we have D(lambda a)=lambda^3 D(a) for all ain A and lambdain C. In this paper, we define linear-cubic map and linear-cubic derivation as follows. We say the cubic homogenous map D:A--->X is a linear-cubic map if we have D(lambda a+b)=lambda^3D(a)+D(b) , for all a,bin A and lambdain C and moreover if D:A--->X is a cubic derivation, then we call it a linear-cubic derivation. In this paper, we characterize linear-cubic derivations on various class of Banach algebras such as Banach algebras obtained by theta-Lau product, module extensions of Banach algebras and amalgamated Banach algebras. For characterizing, we define theta-cubic derivation and module cubic mappings. For Banach algebra Atimes_theta B , where thetainsigma(A)cup{0} and A is unital, we show that D:A--->X is a linear-cubic derivation if and only if there are theat -cubic derivation D_B,A:B--->A and linear-cubic derivations D_A:A--->A and D_B:B---> B such that for any (a,b)in Atimes_theta B, be as follows D(a,b)=(D_A(a)+D_B,A(b),D(b)) and these mappings satisfy in the given condition. We obtain similar results for module extensions of Banach algebras and amalgamated Banach algebras. Manuscript profile
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  3 - On the continuity of some linear maps on certain Banach algebras
  H. Farhadi E. Ghaderi
  10.30495/jlta.2022.1952747.1470
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  4 - Module amenability and module biprojectivity of θ-Lau product of Banach algebras
  D. Ebrahimi Bagha H. Azaraien
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