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Maysam Maysami Sadr

Publications and source records attributed to Maysam Maysami Sadr.

27 records · Page 2Linked to original sources
arXiv2017

Vietoris topology on hyperspaces associated to a noncommutative compact space

We study some topological spaces that can be considered as hyperspaces associated to noncommutative spaces. More precisely, for a NC compact space associated to a unital C*-algebra, we consider the set of closed projections of the second dual of the C*-algebra as the hyperspace of closed subsets of the NC space. We endow this hyperspace with an analog of Vietoris topology. In the case that the NC space has a quantum metric space structure in the sense of Rieffel we study the analogs of Hausdorff and infimum distances on the hyperspace. We also formulate some interesting problems about distances between sub-circles of a quantum torus.

math.OA↗
arXiv2017

Decomposition of functions between Banach spaces in the orthogonality equation

Let $E,F$ be Banach spaces. In the case that $F$ is reflexive we give a description for the solutions $(f,g)$ of the Banach-orthogonality equation $$\langle f(x),g(α)\rangle=\langle x,α\rangle\hspace{10mm}\forall x\in E,\forall α\in E^*,$$ where $f:E\rightarrow F,g:E^*\rightarrow F^*$ are two maps. Our result generalizes the recent result of Łukasik and Wójcik in the case that $E$ and $F$ are Hilbert spaces.

math.FA↗
arXiv2016

Quantum metrics on noncommutative spaces

We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the C*-algebra with itself. We consider some basic properties of these new objects, and state some connections with the Rieffel theory of compact quantum metric spaces. The main gap in our work is the lack of a nonclassical example even in the case of C*-algebras of matrices.

math.OA↗
arXiv2015

On the quantum groups and semigroups of maps between noncommutative spaces

We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P.M. Soltan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite NC space. As special cases three classes of NC objects are introduced: quantum group of gauge transformations, Pontryagin dual of a quantum group, and Galois-Hopf-algebra of an algebra extension.

math.QA↗
arXiv2015

On the stability of a generalized additive functional equation

We consider Hyers-Ulam stability of a functional equation for continuous functions on a space on which a topological group acts, analogous to the additive functional equation on a group. We show, among other things, that our generalized additive equation, for continuous functions on a homogenous space of a strongly amenable topological group, is stable provided that the canonical projection from that group to its homogenous space is a fiber bundle.

math.FA↗
arXiv2012

A Kind of Compact Quantum Semigroups

We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure.

math.OA↗
arXiv2010

Quantum Functor $Mor$

Let $Top_c$ be the category of compact spaces and continuous maps and $Top_f\subset Top_c$ be the full subcategory of finite spaces. Consider the covariant functor $Mor:Top_f^{op}\times Top_c\to Top_c$ that associates any pair $(X,Y)$ with the space of all morphisms from $X$ to $Y$. In this paper, we describe a non commutative version of $Mor$. More pricelessly, we define a functor $\mathfrak{M}\mathfrak{o}\mathfrak{r}$, that takes any pair $(B,C)$ of a finitely generated unital C*-algebra $B$ and a finite dimensional C*-algebra $C$ to the quantum family of all morphism from $B$ to $C$.

math.OA↗