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Journal of the Iranian Mathematical Society (27171612)5(2)pp. 253-260
For a discrete group Γ, a Hopf von Neumann algebra (M, ∆) and a W*-dynamical system (M, Γ, α) such that (Formula Presented)), we show that the crossed product M ⋊α Γ with a comultiplication is a Hopf von Neumann algebra. Furthermore, we prove that the inner amenability of the predual M* is equivalent to the inner amenability of (M ⋊α Γ)*. Finally, we conclude that if the action α: Γ → Aut(ℓ∞(Γ)) is defined by αs(f)(t) = f(s−1ts), then the inner amenability of discrete group Γ is equivalent to the inner amenability of (ℓ∞(Γ) ⋊α Γ)*. © 2024 Iranian Mathematical Society.
Computational Methods For Differential Equations (23453982)11(2)pp. 281-290
A numerical method based on the Haar wavelet is introduced in this study for solving the partial differential equation which arises in the pricing of European options. In the first place, and due to the change of variables, the related partial differential equation (PDE) converts into a forward time problem with a spatial domain ranging from 0 to 1. In the following, the Haar wavelet basis is used to approximate the highest derivative order in the equation concerning the spatial variable. Then the lower derivative orders are approximated using the Haar wavelet basis. Finally, by substituting the obtained approximations in the main PDE and doing some computations using the finite differences approach, the problem reduces to a system of linear equations that can be solved to get an approximate solution. The provided examples demonstrate the effectiveness and precision of the method. © 2023 University of Tabriz. All rights reserved.
Canadian Mathematical Bulletin (14964287)66(3)pp. 927-936
Let be a Banach algebra, and let be a nonzero character on. For a closed ideal I of with such that I has a bounded approximate identity, we show that, the space of weakly almost periodic functionals on, admits a right (left) invariant -mean if and only if admits a right (left) invariant -mean. This generalizes a result due to Neufang for the group algebra as an ideal in the measure algebra, for a locally compact group G. Then we apply this result to the quantum group algebra of a locally compact quantum group. Finally, we study the existence of left and right invariant -means on. © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society.
Mathematica Slovaca (01399918)69(5)pp. 1177-1184
Let L be a Lau algebra and X be a topologically invariant subspace of L containing UC(L). We prove that if L has a bounded approximate identity, then strict inner amenability of L is equivalent to the existence of a strictly inner invariant mean on X. We also show that when L is inner amenable the cardinality of the set of topologically left invariant means on L is equal to the cardinality of the set of topologically left invariant means on RUC(L). Applying this result, we prove that if L is inner amenable and hL2i = L, then the essential left amenability of L is equivalent to the left amenability of L. Finally, for a locally compact group G, we consider the measure algebra M(G) to study strict inner amenability of M(G) and its relation with inner amenability of G. © 2019 Mathematical Institute Slovak Academy of Sciences.
Annals of Functional Analysis (20088752)9(4)pp. 514-524
We initiate a study of operator approximate biprojectivity for quantum group algebra L1(G[double-struck]), where G[double-struck] is a locally compact quantum group. We show that if L1(G[double-struck]) is operator approximately biprojective, then G[double-struck] is compact. We prove that if G[double-struck] is a compact quantum group and is a non-Kac-type compact quantum group such that both L1(G[double-struck]) and L1 are operator approximately biprojective, then L1(G[double-struck])⊗ L1 is operator approximately biprojective, but not operator biprojective. © 2018 by the Tusi Mathematical Research Group.
Canadian Mathematical Bulletin (14964287)60(1)pp. 122-130
We characterize two important notions of amenability and compactness of a locally compact quantum group G in terms of certain homological properties. For this, we show that G is character amenable if and only if it is both amenable and co-amenable. We finally apply our results to Arens regularity problems of the quantum group algebra L1(G). In particular, we improve an interesting result by Hu, Neufang, and Ruan. © 2016 Canadian Mathematical Society.
International Journal of Mathematics (17936519)24(7)
We initiate a study of inner amenability for a locally compact quantum group G in the sense of Kustermans-Vaes. We show that all amenable and co-amenable locally compact quantum groups are inner amenable. We then show that inner amenability of G is equivalent to the existence of certain functionals associated to characters on L1(G). For co-amenable locally compact quantum groups, we introduce and study strict inner amenability and its relation to the extension of the co-unit ε from C0(G) to L ∞(G). We then obtain a number of equivalent statements describing strict inner amenability of G and the existence of certain means on subspaces of L∞(G) such as LUC(G), RUC(G) and UC(G). Finally, we offer a characterization of strict inner amenability in terms of a fixed point property for L1(G)-modules. © 2013 World Scientific Publishing Company.
Studia Scientiarum Mathematicarum Hungarica (15882896)50(1)pp. 26-30
For two locally compact groups G and H, we show that if L1(G) is strictly inner amenable, then L1(G × H) is strictly inner amenable. We then apply this result to show that there is a large class of locally compact groups G such that L1(G) is strictly inner amenable, but G is not even inner amenable. © 2013 Akadémiai Kiadó, Budapest.
