Weak module amenability of triangular banach algebras II
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Ebrahim Nasrabadi
Abstract
Let A and B be Banach 𝔄-bimodule and Banach 𝔅-bimodule algebras, respectively. Also let M be a Banach A, B-module and Banach 𝔄, 𝔅-module with compatible actions. In the case of 𝔄 = 𝔅, the author along with Pourabbas [5] have studied the weak 𝔄-module amenability of triangular Banach algebra
In this paper we investigate a special structure of 𝔄 ⊕ 𝔅-bimodule derivation from 𝓣 into 𝓣∗ and show that 𝓣 is weakly 𝔄 ⊕ 𝔅-bimodule amenable if and only if the corner Banach algebras A and B are weakly 𝔄-module amenable and weakly 𝔅-module amenable, respectively, where A, B and M are essential and not necessary unital.
(Communicated by Gregor Dolinar)
References
[1] Amini, M.: Module amenability for semigroup algebras, Semigroup Forum 69 (2004), 243–254.10.1007/s00233-004-0107-3Suche in Google Scholar
[2] Amini, M.—Bagha, B. E.: Weak module amenability for semigroup algebras, Semigroup Forum 71 (2005), 18–26.10.1007/s00233-004-0166-5Suche in Google Scholar
[3] Forrest, B. E.— Marcoux, L. W.: Weak amenability of triangular Banach algebras, Trans. Amer. Math. Soc. 345 (2002), 1435–1452.10.1090/S0002-9947-01-02957-9Suche in Google Scholar
[4] Johnson, B. E.: Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).10.1090/memo/0127Suche in Google Scholar
[5] Pourabbas, A. R.— Nasrabadi, E.: Weak module amenability of triangular Banach algebras, Math. Slovaca 61 (2011), 949–958.10.2478/s12175-011-0061-ySuche in Google Scholar
© 2019 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- RNDr. Miloslav Duchoň, DrSc. passed away ∗ aug. 21, 1932 – †dec. 31, 2018
- Prof. RNDr. Gejza Wimmer, DrSc. – A Septuagenerian?
- Two monads on the category of graphs
- Entropy of MV-algebraic dynamical systems: An example
- Going up and lying over in congruence-modular algebras
- The minimal arity of near unanimity polymorphisms
- On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one
- The generalized Fermat Conjecture
- Evaluation of sums involving products of Gaussian q-binomial coefficients with applications
- Integrals of logarithmic functions and alternating multiple zeta values
- An abelian subextension of the dyadic division field of a hyperelliptic Jacobian
- The class of all semigroups related to semihypergroups of order 2
- Criterion for the weak potency of certain HNN extensions
- Fekete Szegö theorem for a close-to-convex error function
- Bounds for distance between eigenvalues of boundary value problems with retarded argument
- Gradient estimates for a nonlinear heat equation under the Finsler-Ricci flow
- Weak module amenability of triangular banach algebras II
- Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class
- Example of C-rigid polytopes which are not B-rigid
- Some comments on rU-spaces
- On the equivalence of various definitions of mixed poisson processes
- A note on discrete C-embedded subspaces
Artikel in diesem Heft
- Regular papers
- RNDr. Miloslav Duchoň, DrSc. passed away ∗ aug. 21, 1932 – †dec. 31, 2018
- Prof. RNDr. Gejza Wimmer, DrSc. – A Septuagenerian?
- Two monads on the category of graphs
- Entropy of MV-algebraic dynamical systems: An example
- Going up and lying over in congruence-modular algebras
- The minimal arity of near unanimity polymorphisms
- On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one
- The generalized Fermat Conjecture
- Evaluation of sums involving products of Gaussian q-binomial coefficients with applications
- Integrals of logarithmic functions and alternating multiple zeta values
- An abelian subextension of the dyadic division field of a hyperelliptic Jacobian
- The class of all semigroups related to semihypergroups of order 2
- Criterion for the weak potency of certain HNN extensions
- Fekete Szegö theorem for a close-to-convex error function
- Bounds for distance between eigenvalues of boundary value problems with retarded argument
- Gradient estimates for a nonlinear heat equation under the Finsler-Ricci flow
- Weak module amenability of triangular banach algebras II
- Some consequences of quasicentral approximate units modulo Hilbert-Schmidt class
- Example of C-rigid polytopes which are not B-rigid
- Some comments on rU-spaces
- On the equivalence of various definitions of mixed poisson processes
- A note on discrete C-embedded subspaces
