Ramezanpour, M. Character Connes amenability of dual Banach algebras (2018) Czechoslovak Mathematical Journal, 68 (1), pp. 243-255.
DOI: 10.21136/CMJ.2018.0451-16
ABSTRACT We study the notion of character Connes amenability of dual Banach algebras and show that if A is an Arens regular Banach algebra, then A** is character Connes amenable if and only if A is character amenable, which will resolve positively Runde’s problem for this concept of amenability. We then characterize character Connes amenability of various dual Banach algebras related to locally compact groups. We also investigate character Connes amenability of Lau product and module extension of Banach algebras. These help us to give examples of dual Banach algebras which are not Connes amenable. © 2018, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.
AUTHOR KEYWORDS: character amenability; Connes amenability; dual Banach algebra; locally compact group
PUBLISHER: Springer New York LLC
Ramezanpour, M. More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphism (2018) Mathematica Slovaca, 68 (1), pp. 147-152.
DOI: 10.1515/ms-2017-0087
ABSTRACT For two Banach algebras A and B, the T-Lau product A×T B, was recently introduced and studied for some bounded homomorphism T : B → A with T ≤ 1. Here, we give general nessesary and sufficent conditions for A×T B to be (approximately) cyclic amenable. In particular, we extend some recent results on (approximate) cyclic amenability of direct product A B and T-Lau product A×T B and answer a question on cyclic amenability of A×T B. © 2018 Mathematical Institute Slovak Academy of Sciences.
AUTHOR KEYWORDS: approximate cyclic amenability; Banach algebra; cyclic amenability; T-Lau product
PUBLISHER: De Gruyter Open Ltd
Ramezanpour, M., Barootkoob, S. Generalized module extension Banach algebras: Derivations and weak amenability (2017) Quaestiones Mathematicae, 40 (4), pp. 451-465.
DOI: 10.2989/16073606.2017.1296902
ABSTRACT Let A and X be Banach algebras and let X be an algebraic Banach A-module. Then the ℓ1-direct sum A × X equipped with the multiplication (Figure presented.) is a Banach algebra, denoted by A ⋈ X, which will be called “a generalized module extension Banach algebra”. Module extension algebras, Lau product and also the direct sum of Banach algebras are the main examples satisfying this framework. We characterize the structure of n-dual valued (n ∈ ℕ) derivations on A ⋈ X from which we investigate the n-weak amenability for the algebra A ⋈ X. We apply the results and the techniques of proofs for presenting some older results with simple direct proofs. © 2017 NISC (Pty) Ltd.
AUTHOR KEYWORDS: Banach algebra; derivation; n-weak amenability
PUBLISHER: Taylor and Francis Ltd.
Ramezanpour, M. Weak amenability of the Lau product of Banach algebras defined by a Banach algebra morphism (2017) Bulletin of the Korean Mathematical Society, 54 (6), pp. 1991-1999.
DOI: 10.4134/BKMS.b160690
ABSTRACT Let A and B be two Banach algebras and T: B → A be a bounded homomorphism, with ∥T ∥ ≤ 1. Recently, Dabhi, Jabbari and Haghnejad Azar (Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 9, 1461– 1474) obtained some results about the n-weak amenability of A ×T B. In the present paper, we address a gap in the proof of these results and extend and improve them by discussing general necessary and sufficient conditions for A ×T B to be n-weakly amenable, for an integer n ≥ 0. © 2017 Korean Mathematical Society.
AUTHOR KEYWORDS: Banach algebra; Derivation; T-Lau product; Weak amenability
PUBLISHER: Korean Mathematical Society
Ramezanpour, M. Derivations into various duals of Lau product of Banach algebras (2017) Publicationes Mathematicae, 90 (3-4), pp. 493-505.
DOI: 10.5486/PMD.2017.7692
ABSTRACT For two Banach algebras A and B, an interesting product A× θB, called the θ -Lau product, was recently introduced and studied for some non-zero multiplicative linear functional θ on B. In this paper, by discussing general necessary and sufficient conditions for n-weak amenability of A× θ B, we extend some results on the n-weak amenability of the unitization A# of A, to the θ -Lau product A× θ B. In particular, we improve several known results on n-weak amenability of A× θ B and answer some questions on this topic. © 2017 University of Debrecen, Institute of Mathematics.
AUTHOR KEYWORDS: Banach algebra; Derivation; N-weak amenability
PUBLISHER: University of Debrecen, Institute of Mathematics
Ramezanpour, M., Tavallaei, N., Olfatian Gillan, B. Character amenability and contractibility of some banach algebras on left coset spaces (2016) Annals of Functional Analysis, 7 (4), pp. 564-572.
DOI: 10.1215/20088752-3661431
ABSTRACT Let H be a compact subgroup of a locally compact group G, and let μ be a strongly quasi-invariant Radon measure on the homogeneous space G/H. In this article, we show that every element of G/H, the character space of G/H, determines a nonzero multiplicative linear functional on L1(G/H μ). Using this, we prove that for all ⌽ ε G/H, the right φ-amenability of L1(G/H; μ) and the right φ-amenability of M(G/H) are both equivalent to the amenability of G. Also, we show that L1(G/H; μ), as well as M(G=H), is right φ-contractible if and only if G is compact. In particular, when H is the trivial subgroup, we obtain the known results on group algebras and measure algebras. © 2016 by the Tusi Mathematical Research Group.
AUTHOR KEYWORDS: Banach algebra; Character amenability; Homogeneous space
PUBLISHER: Duke University Press
Ramezanpour, M. On action of Lau algebras on von Neumann algebras (2015) Bulletin of the Korean Mathematical Society, 52 (2), pp. 557-570.
DOI: 10.4134/BKMS.2015.52.2.557
ABSTRACT Let G be a von Neumann algebraic locally compact quan- tum group, in the sense of Kustermans and Vaes. In this paper, as a consequence of a notion of amenability for actions of Lau algebras, we show that bG, the dual of G, is co-amenable if and only if there is a state m 2 L∞(Ĝ)∗ which is invariant under a left module action of L1(G) on L∞(Ĝ)∗. This is the quantum group version of a result by Stokke [17]. We also characterize amenable action of Lau algebras by several proper- ties such as fixed point property. This yields in particular, a fixed point characterization of amenable groups and H-amenable representation of groups. © 2015 Korean Mathematical Society.
AUTHOR KEYWORDS: Amenability; Hopf von Neumann algebra; Lau algebra; Locally compact quantum group; Unitary representation
PUBLISHER: Korean Mathematical Society
Tavallaei, N., Ramezanpour, M., Gillan, B.O. Structural transition between Lp(G) and Lp(G/H) (2015) Banach Journal of Mathematical Analysis, 9 (3), pp. 194-205.
DOI: 10.15352/bjma/09-3-14
ABSTRACT Let H be a compact subgroup of a locally compact group G. We consider the homogeneous space G/H equipped with a strongly quasi-invariant Radon measure μ. For 1 ≤ p ≤ +∞, we introduce a norm decreasing linear map from Lp(G) onto Lp(G/H, μ) and show that Lp(G/H, μ) may be identified with a quotient space of Lp(G). Also, we prove that Lp(G/H, μ) is isometrically isomorphic to a closed subspace of Lp(G). These help us study the structure of the classical Banach spaces constructed on a homogeneous space via those created on topological groups.
AUTHOR KEYWORDS: Classical Banach space; Homogeneous space; Locally compact topological group; Strongly quasi-invariant measure
PUBLISHER: Duke University Press
Ramezanpour, M., Vishki, H.R.E. Reiter's properties for the actions of locally compact quantum groups on von Neumann algebras (2010) Bulletin of the Iranian Mathematical Society, 36 (2), pp. 1-17.
ABSTRACT The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter's conditions for such an action are discussed. Several applications to some specific actions related to certain representations and core presentaions are presented. © 2010 Iranian Mathematical Society.
AUTHOR KEYWORDS: Action; Amenability; Locally compact quantum group; Unitary core presentation
Tabadkan, G.A., Ramezanpour, M. A fixed point approach to the stability of φ-morphisms on hilbert c*-modules (2010) Annals of Functional Analysis, 1 (1), pp. 44-50.
DOI: 10.15352/afa/1399900992
ABSTRACT Let E, F be two Hilbert C*-modules over C*-algebras A and B respectively. In this paper, by the alternative fixed point theorem, we give the Hyers–Ulam–Rassias stability of the equation 〈U(x), U(y)〉 = φ(〈x, y〉) (x, y ∈ E), where U: E → F is a mapping and φ: A → B is an additive map. © 2010, Duke University Press. All rights reserved.
AUTHOR KEYWORDS: Hilbert C*-modules; Hyers-Ulam-Rassias stability