Related papers: A new approach to convolution and semi-direct prod…

Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\mu)$ such that the Banach space…

Let $H$ and $K$ be locally compact groups and also $\tau:H\to Aut(K)$ be a continuous homomorphism and $G_\tau=H\ltimes_\tau K$ be the semi-direct product of $H$ and $K$ with respect to the continuous homomorphism $\tau$. This paper…

For a locally compact group $G$ and a compact subgroup $H$, we show that the Banach space $M(G/H)$ may be considered as a quotient space of $M(G)$. Also, we define a convolution on $M(G/H)$ which makes it into a Banach algebra. It may be…

Our goal is to find classes of convolution semigroups on Lie groups $G$ that give rise to interesting processes in symmetric spaces $G/K$. The $K$-bi-invariant convolution semigroups are a well-studied example. An appealing direction for…

The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\mathfrak q$ (= $\mathfrak q$-invariants in the symmetric algebra $S(\mathfrak…

We define a Fourier transform and a convolution product for functions and distributions on Heisenberg--Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for…

Let $k$ be an algebraically closed base field of characteristic zero. The category equivalence between central simple algebras and irreducible, generically free $PGL_n$-varieties is extended to the context of central simple algebras with…

Let A and U be Banach algebras such that U is also a Banach A- bimodule with compatible algebra operations, module actions and norm. By defining an approprite action, we turn l1-direct product A item U into a Banach algebra such that A is…

Let $H$ be a locally compact group, $K$ be an LCA group, $\tau:H\to Aut(K)$ be a continuous homomorphism and $G_\tau=H\ltimes_\tau K$ be the semi-direct product of $H$ and $K$ with respect to the continuous homomorphism $\tau$. In this…

We define a trivolution on a complex algebra $A$ as a non-zero conjugate-linear, anti-homomorphism $\tau$ on $A$, which is a generalized inverse of itself, that is, $\tau^3=\tau$. We give several characterizations of trivolutions and show…

Let $G$ be a locally compact group and $A$ be a commutative semisimple Banach algebra over the scalar field $\mathbb{C}$. The correlation between different types of $BSE$- Banach algebras $A$, and the Banach algebras $L^{1}(G, A)$ are…

Let $({\sf G},\alpha, \omega,\mathfrak B)$ be a measurable twisted action of the locally compact group ${\sf G}$ on a Banach $^*$-algebra $\mathfrak B$ and $\mathfrak A$ a differential Banach $^*$-subalgebra of $\mathfrak B$, which is…

We consider the semi-direct products $G=\mathbb Z^2\rtimes GL_2(\mathbb Z), \mathbb Z^2\rtimes SL_2(\mathbb Z)$ and $\mathbb Z^2\rtimes\Gamma(2)$ (where $\Gamma(2)$ is the congruence subgroup of level 2). For each of them, we compute both…

Let $ H $ be a compact subgroup of a locally compact group $G$. In this paper we define a convolution on $ M(G/H) $, the space of all complex bounded Radon measures on the homogeneous space G/H. Then we prove that the measure space $ M(G/H,…

We introduce and study a new Banach algebra structure on the trace-zero subspace $\mathcal{T}(L^2(\mathbb{G}))_0$ of trace class operators for any locally compact quantum group $\mathbb{G}$; it is defined through a mixed Lie-type product of…

Let G be a locally compact group. Consider the Banach algebra L_1(G)^**, equipped with the first Arens multiplication, as well as the algebra LUC(G)^*, the dual of the space of bounded left uniformly continuous functions on G, whose product…

Let $H$ be a locally compact group and $K$ be an LCA group also let $\tau:H\to Aut(K)$ be a continuous homomorphism and $G_\tau=H\ltimes_\tau K$ be the semidirect product of $H$ and $K$ with respect to $\tau$. In this article we define the…

This article is intended towards the study of the bidual of generalized group algebra $L^1(G,\mA)$ equipped with two Arens product, where $G$ is any locally compact group and $\mA$ is a Banach algebra. We show that the left topological…

Letting tau denote the inverse transpose automorphism of GL(n,q), a formula is obtained for the number of g in GL(n,q) so that gg^{tau} is equal to a given element h. This generalizes a result of Gow and Macdonald for the special case that…

Let $A$ and $B$ be Banach algebras and let $T$ be an algebra homomorphism from $B$ into $A$. The Cartesian product space $A\times B$ by $T$- Lau product and $\ell^{1}$- norm becomes a Banach algebra $A\times_{T}B$. We investigate the…