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The contribution of this work is twofold. The first part deals with a Hilbert-space version of McCann's celebrated result on the existence and uniqueness of monotone measure-preserving maps: given two probability measures $\rm P$ and $\rm…

Probability · Mathematics 2023-05-23 Alberto González-Sanz , Marc Hallin , Bodhisattva Sen

As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or corank, here we consider the problem inbetween, that is, we treat the question of preserving operators…

Operator Algebras · Mathematics 2007-05-23 Lajos Molnar

The paper is devoted to the problem of classification of extremal positive maps acting between $B(K)$ and $B(H)$ where $K$ and $H$ are Hilbert spaces. It is shown that every positive map with the property that $\rank \phi(P)\leq 1$ for any…

Operator Algebras · Mathematics 2014-06-17 Marcin Marciniak

Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…

Algebraic Topology · Mathematics 2024-11-04 Steve Oudot

We show that smooth maps are $C^1$-dense among $C^1$ volume preserving maps.

Dynamical Systems · Mathematics 2008-10-10 Artur Avila

We introduce a preorder relation in the collection of all operator valued completely positive maps on a full Hilbert C*-module and characterize this relation in terms of the Stinespring construction associated to each completely positive…

Operator Algebras · Mathematics 2018-06-18 Maria Joiţa

The aim of this article is to extend the results of Asadi M.B, B.V.R. Bhat, G. Ramesh, K. Sumesh about completely positive maps on Hilbert C*-modules. We prove a Stinespring type theorem for a finite family of completely positive maps on…

Operator Algebras · Mathematics 2012-10-23 Marat Pliev

We introduce and study some new uniform structures for Hilbert $C^*$-modules over an algebra $A$. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of…

Operator Algebras · Mathematics 2024-02-29 Denis Fufaev , Evgenij Troitsky

Let $A$ be a (non-unital, in general) C*-algebra with center $Z(M(A))$ of its multiplier algebra, and let $\{ X, \langle .,. \rangle \}$ be a full Hilbert $A$-module. Then any bijective bounded module morphism $T$, for which every…

Operator Algebras · Mathematics 2026-04-09 Michael Frank

The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital…

Operator Algebras · Mathematics 2025-05-08 Michael Frank , David R. Larson

The aim of this paper is to present a unified framework in the setting of Hilbert $C^*$-modules for the scalar- and vector-valued reproducing kernel Hilbert spaces and $C^*$-valued reproducing kernel spaces. We investigate conditionally…

Operator Algebras · Mathematics 2021-05-17 M. S. Moslehian

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…

Operator Algebras · Mathematics 2025-05-08 Michael Frank , David R. Larson

Ranking data arises in a wide variety of application areas but remains difficult to model, learn from, and predict. Datasets often exhibit multimodality, intransitivity, or incomplete rankings---particularly when generated by humans---yet…

Machine Learning · Computer Science 2019-01-29 Stephen Ragain , Johan Ugander

Extending Wigner's theorem we give a characterization of positive maps of $B(H)$ into itself which map the set of rank k projections onto itself.

Operator Algebras · Mathematics 2016-04-21 Erling Størmer

Constructive proofs of fact that a stably free left $S$-module $M$ with rank$(M)\geq$sr$(S)$ is free, where sr$(S)$ denotes the stable rank of an arbitrary ring $S$, were developed in some articles. Additionally, in such papers, are…

Rings and Algebras · Mathematics 2015-10-20 Claudia Gallego

In this paper, we study the representation of orthogonally additive mappings acting on Hilbert $C^*$-modules and Hilbert $H^*$-modules. One of our main results shows that every continuous orthogonally additive mapping $f$ from a Hilbert…

Operator Algebras · Mathematics 2013-04-29 Dijana Ilisevic , Aleksej Turnsek , Dilian Yang

We study the structure and compute the stable rank of C*-algebras of finite higher-rank graphs. We completely determine the stable rank of the C*-algebra when the k-graph either contains no cycle with an entrance, or is cofinal. We also…

Operator Algebras · Mathematics 2021-09-08 David Pask , Adam Sierakowski , Aidan Sims

The paper is devoted to continuous frames and Riesz bases in Hilbert C*-modules. we define a continuous Riesz basis for Hilbert C*-modules and give some results about them.

Functional Analysis · Mathematics 2022-09-20 Hadi Ghasemi , Tayebe Lal Shateri

We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra $A(\alpha,\beta,\gamma)$ has a non-free, stably free right ideal. Further, we compute…

Rings and Algebras · Mathematics 2017-07-24 Claudia Gallego , Andrea Solotar

This study aims at combining the concepts of $g$-frame and $K$-frame for a Hilbert $C^*$-module $U$, for an operator $K \in End^*_A(U)$, where $End^*_A(U)$ contains all adjointable $A$-linear maps on $U$. As a result, continuous…

Functional Analysis · Mathematics 2024-10-07 Jahangir Cheshmavar , Javad Baradaran , Asadollah Hossienpour