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We study equivariant morphisms from zero dimensional schemes to varieties and show that, under suitable assumptions, all such morphisms factor via a canonical one. We relate the above to Algebraic Representations of Ergodic Actions.

Algebraic Geometry · Mathematics 2023-04-05 Avraham Aizenbud , Uri Bader

We prove that an operator space is completely isometric to a ternary ring of operators if and only if the open unit balls of all of its matrix spaces are bounded symmetric domains. From this we obtain an operator space characterization of…

Operator Algebras · Mathematics 2007-05-23 Matthew Neal , Bernard Russo

We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…

Mathematical Physics · Physics 2011-11-22 Janusz Grabowski , Marek Kus , Giuseppe Marmo

In this paper, we prove that unital homomorphisms from continuous functions on a compact metric space to matrices over a C*-algebra with tracial rank at most one are approximately diagonalizable. We also consider some generalizations of…

Operator Algebras · Mathematics 2017-03-13 Min Ro

The main results of this paper show that various coarse (`large scale') geometric properties are closely related. In particular, we show that property A implies the operator norm localisation property, and thus that norms of operators…

Metric Geometry · Mathematics 2012-03-29 Jacek Brodzki , Graham A. Niblo , Jan Spakula , Rufus Willett , Nick J. Wright

We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…

Representation Theory · Mathematics 2020-12-29 Victor A. Bovdi , Tetiana Klymchuk , Tetiana Rybalkina , Mohamed A. Salim , Vladimir V. Sergeichuk

Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a…

Operator Algebras · Mathematics 2007-05-23 E. Andruchow , G. Corach , D. Stojanoff

A general framework for the description of the physical properties of matter by a canonical reduction procedure of tensors is presented; besides geometrical symmetries, this paper emphasizes the role of intrinsic symmetries which are due…

General Physics · Physics 2019-01-09 R. Bonneville

Two approaches are developed to exploit, for simple complex or compact real Lie algebras g, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as…

Mathematical Physics · Physics 2007-05-23 A. J. Macfarlane , H. Pfeiffer

Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for…

Functional Analysis · Mathematics 2015-11-09 Jagjit Singh Matharu , Mohammad Sal Moslehian

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A_1 and A_2 are operator algebras, then any bounded epimorphism of A_1 onto A_2 is completely bounded provided that A_2…

Operator Algebras · Mathematics 2016-05-13 David R. Pitts

We prove a quantized version of a theorem by M. V. Sheinberg: A uniform algebra equipped with its canonical, i.e. minimal, operator space structure is operator amenable if and only if it is a commutative $C^\ast$-algebra.

Functional Analysis · Mathematics 2007-05-23 Volker Runde

Kadison and Kastler introduced a metric on the set of all C$^*$-algebras on a fixed Hilbert space. In this paper structural properties of C$^*$-algebras which are close in this metric are examined. Our main result is that the property of…

Operator Algebras · Mathematics 2010-08-16 Erik Christensen , Allan Sinclair , Roger R. Smith , Stuart White

We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…

Analysis of PDEs · Mathematics 2011-03-02 H. -J. Flad , G. Harutyunyan , B. -W. Schulze

We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This…

Mathematical Physics · Physics 2013-11-07 Aleksandr L. Lisok , Aleksandr V. Shapovalov , Andrey Yu. Trifonov

This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…

Quantum Physics · Physics 2007-05-23 Timothy F. Havel , Chris J. L. Doran

We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…

Functional Analysis · Mathematics 2014-10-21 Shigeru Furuichi

Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…

General Relativity and Quantum Cosmology · Physics 2007-05-23 E. A. Tagirov

We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…

Logic · Mathematics 2013-08-29 Tarek Sayed Ahmed

A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space $C^*$-algebras are isomorphic. An improved characterization of simplicity for labelled space $C^*$-algebras…

Operator Algebras · Mathematics 2019-09-11 Gilles G. de Castro , Daniel W. van Wyk