Javanshiri, H., Tavallaei, N. Some properties of LUC(X,G)∗ as a banach left LUC(G)∗-module (2018) Semigroup Forum, pp. 1-24. Article in Press.
DOI: 10.1007/s00233-018-9947-0
ABSTRACT Associated with a locally compact group (Formula presented.) and a (Formula presented.)-space (Formula presented.) there is a Banach subspace (Formula presented.) of (Formula presented.), which has been introduced and studied by Chu and Lau (Math Z 268:649–673, 2011). In this paper, we study some properties of the first dual space of (Formula presented.). In particular, we introduce a left action of (Formula presented.) on (Formula presented.) to make it a Banach left module and then we investigate the Banach subalgebra (Formula presented.) of (Formula presented.), as the topological centre related to this module action, which contains (Formula presented.) as a closed subalgebra. Also, we show that the faithfulness of this module action is related to the properties of the action of (Formula presented.) on (Formula presented.) and we prove an analogue of the main result of Lau (Math Proc Cambridge Philos Soc 99:273–283, 1986) for (Formula presented.)-spaces. Sufficient and/or necessary conditions for the equality (Formula presented.) or (Formula presented.) are given. Finally, we apply our results to some special cases of (Formula presented.) and (Formula presented.) for obtaining various examples whose topological centres (Formula presented.) are (Formula presented.), (Formula presented.) or neither of them. © 2018 Springer Science+Business Media, LLC, part of Springer Nature
AUTHOR KEYWORDS: $$mathcal G$$G-space; Complex radon measure; Left module action; Left uniformly continuous function; Measure algebra; Topological centre PUBLISHER: Springer New York LLC
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
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
Arefijamaal, A.A., Tavallaei, N. Continuous frame wavelets (2012) Acta Mathematica Scientia, 32 (2), pp. 807-812.
DOI: 10.1016/S0252-9602(12)60061-7
ABSTRACT Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ ∈ H is called a continuous frame wavelet if there exist A,B > 0 such that. in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components. © 2012 Wuhan Institute of Physics and Mathematics.
AUTHOR KEYWORDS: Continuous frame; Direct integral; Locally compact group; Unitary representation; Wavelet transform
Kamyabi-Gol, R.A., Tavallaei, N. Convolution and homogeneous spaces (2009) Bulletin of the Iranian Mathematical Society, 35 (1), pp. 129-146.
ABSTRACT Let G be a locally compact Hausdorff topological group and H be a compact subgroup of G. Then, the homogeneous space G/H possesses a specific Radon measure, which is called a relatively invariant measure. We show that the concepts of convolution and involution can be extended to the integrable functions defined on this homogeneous space. We study the properties of convolution and prove that the space of integrable functions is an involutive Banach algebra with an approximate identity. We also find a necessary and sufficient condition on a closed subspace of this Banach algebra to make it a left ideal. © 2009 Iranian Mathematical Society.
AUTHOR KEYWORDS: Convolution; Homogeneous space; Integrable function; Involutive Banach algebra; Relatively invariant measure; Rho-function; Strongly quasi-invariant measure