arXiv subjects

Choiti Bandyopadhyay

Publications and source records attributed to Choiti Bandyopadhyay.

6 recordsLinked to original sources

arXiv2024

Common Fixed Points of Semihypergroup Representations

In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of semihypergroup actions on a general topological space and discussed different continuity, equivalence and natural fixed point properties of the same in [6]. Now in this article, we consider different kinds of representations of a semihypergroup on compact convex subsets of a locally convex space and explore equivalence relations between certain fixed-point properties of such representations and amenability of the space of almost periodic functions. Finally, we investigate how far these equivalence relations can be strengthened when in particular, we consider representations on the dual of a Banach space.

math.FA↗

arXiv2023

Topological Amenability of Semihypergroups

In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of convergence of certain probability measures, total variation of convolution with probability measures and translation of certain functionals, as well as the F-algebraic properties of the associated measure algebra. We further investigate the interplay between restriction of convolution product and convolution of restrictions of measures on a sub-semihypergroup. Finally, we discuss and characterize topological amenability of sub-semihypergroups in terms of certain invariance properties attained on the corresponding measure algebra of the parent semihypergroup. This in turn provides us with an affirmative answer to an open question posed by J. Wong in 1980.

math.FA↗

arXiv2022

Analysis on Semihypergroups: Function Spaces, Homomorphisms and Ideals

The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and analytic structures on semihypergroups, which are well-known in the case of topological groups and semigroups. In particular, we first study almost periodic and weakly almost periodic function spaces (basic properties, their relation to the compactness of the underlying space, introversion and Arens product on their duals among others). We then introduce homomorphisms and ideals, and thereby examine their behaviour (basic properties, structure of the kernel and relation of amenability to minimal ideals) in order to gain insight into the structure of a Semihypergroup itself. In the process, we further investigate where and why this theory deviates from the classical theory of semigroups.

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arXiv2022

Free Product on Semihypergroups

In a previous paper [1] [MR4101040], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate free structures on the category of semihypergroups. We show that the natural free product structure along with the natural topology, although fails to give a free product for topological groups, works well on a vast non-trivial class of `pure' semihypergroups containing most of the well-known examples including non-trivial coset and orbit spaces.

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arXiv2022

Equality in Hausdorff-Young for Hypergroups

It has been shown in "On the Hausdorff-Young theorem for commutative hypergroups" by Sina Degenfeld-Schonburg, that one can extend the domain of Fourier transform of a commutative hypergroup $K$ to $L^p(K)$ for $1\leq p \leq 2$, and the Hausdorff-Young inequality holds true for these cases. In this article, we examine the structure of non-zero functions in $L^p(K)$ for which equality is attained in the Hausdorff-Young inequality, for $1<p<2$, and further provide a characterization for the basic uncertainty principle for commutative hypergroups with non-trivial centre.

math.FA↗

arXiv2022

Fixed Points and Continuity of Semihypergroup Actions

In a couple of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In this article, we introduce and examine (separately) continuous actions on the category of semihypergroups. In particular, we discuss the continuity properties of such actions and explore the equivalence relations between different fixed-point properties of certain actions and the existence of left-invariant mean(s) on the space of almost periodic functions on a semihypergroup.

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