Massoud Amini
It is known that the generator of a strictly continuous one parameter unitary group in the multiplier algebra of a $C^{*}$-algebra is affiliated to that $C^{*}$-algebra . We show that under natural non degeneracy conditions, this self adjoint unbounded operator lies indeed in the (unbounded) multiplier algebra of the Pedersen's ideal of the $C^{*}$-algebra.
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This paper extends a version of the Stone-Weierstrass theorem to more general C*-algebras. Namely, assume that A is a unital, not necessarily separable, C*-algebra, and B is a C*-subalgebra containing the unit element. Then, I prove that: If B separates the factorial states of A, then B=A. This generalizes a result of Popa and Longo for the case when A is separable. A true Stone-Weierstrass theorem would state that, if B separates the pure states of A, then B=A. This problem is open even in the separable case. The present paper relies on the more technical, foundational results in the companio…
Surjective isometries between unital C*-algebras were classified in 1951 by Kadison. In 1972 Paterson and Sinclair handled the nonunital case by assuming Kadison's theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon and the author, producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate how our techniques may be applied to classify surjective isometries of noncommutative Lp spaces, extending some recent results of …
In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we prove that the structure of the liminal $C^{*}$-algebras $\cal A$ determines the topology of its primitive ideal space.
In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we give a partial answere to the question 2.1 of [13], and we prove that the structure of the postliminal C*-algebras A determines the topology of its primitive ideals space.
For a $C_0(X)$-algebra $A$, we study $C(K)$-algebras $B$ that we regard as compactifications of $A$, generalising the notion of (the algebra of continuous functions on) a compactification of a completely regular space. We show that $A$ admits a Stone-Čech-type compactification $A^β$, a $C(βX)$-algebra with the property that every bounded continuous section of the C$^*$-bundle associated with $A$ has a unique extension to a continuous section of the bundle associated with $A^β$. Moreover, $A^β$ satisfies a maximality property amongst compactifications of $A$ (with respect to appropriately chose…
From Kümmerer's investigations on stationary Markov processes has emerged an operator algebraic definition of white noises which captures many examples from classical as well as from non-commutative probability. Within non-commutative $L^p$-spaces associated to a white noise, the role of (non-)commutative Lévy processes is played by additive cocycles for the white noise shift, and moreover, the notion for exponentials of classical Lévy processes is generalized by unitary cocycles. As a main result we report a bijective correspondence between additive and unitary cocycles for white noise shifts…
The Covariant Stone-von Neumann Theorem for Locally Compact Quantum Groups
本文将 Stone-von Neumann 定理推广至 Hilbert 模块上的局部紧量子动力学系统，引入一对模表示以涵盖多种模型，并提出了识别强正则局部紧量子群的新准则。
Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Doering, as an alternative mathematical structure within which to formulate physical theories. In particular, it has been used to reformulate standard quantum mechanics in such a way that a novel type of logic is used to represent propositions. In recent years the topic has been considerably progressing with the introduction of probabilities, group and group transformations. In the present paper we will introduce a candidate for the complex quantity value object and analyse its relation to the real quantity v…
In this paper, we use the tools of nonabelian duality to formulate and prove a far-reaching generalization of the Stone-von Neumann Theorem to modular representations of actions and coactions of locally compact groups on elementary $ C^{\ast} $-algebras. This greatly extends the Covariant Stone-von Neumann Theorem for Actions of Abelian Groups recently proven by L. Ismert and the second author. Our approach is based on a new result about Hilbert $ C^{\ast} $-modules that is simple to state yet is widely applicable and can be used to streamline many previous arguments, so it represents an impro…
In this paper, we formulate and prove a version of the Stone-von Neumann Theorem for every $ C^{\ast} $-dynamical system of the form $ (G,\mathbb{K}(\mathcal{H}),α) $, where $ G $ is a locally compact Hausdorff abelian group and $ \mathcal{H} $ is a Hilbert space. The novelty of our work stems from our representation of the Weyl Commutation Relation on Hilbert $ \mathbb{K}(\mathcal{H}) $-modules instead of just Hilbert spaces, and our introduction of two additional commutation relations, which are necessary to obtain a uniqueness theorem. Along the way, we apply one of our basic results on Hil…
\noindent{In} this paper, we clarify the structure of the Stone spectrum of an arbitrary finite von Neumann algebra $\rr$ of type $\rm{I}_{n}$. The main tool for this investigation is a generalized notion of rank for projections in von Neumann algebras of this type.
The aim of this paper is to present some properties of Choquet maximal Radon probability measures on compact, convex subsets of Hausdorff, locally convex, topological real vector spaces. Theorem 3.12 is the main result of the paper. While somewhat technical, the results here are foundational for my proof of a Stone-Weierstrass theorem for non-separable C*-algebras, in the companion paper 'On the Stone-Weierstrass theorem'.
Elliott dimension drop interval algebra is an important class among all $C^*$-algebras in the classification theory. Especially, they are building stones of $\mathcal{AHD}$ algebra and the latter contains all $AH$ algebras with the ideal property of no dimension growth. In this paper, we will show two decomposition theorems related to the Elliott dimension drop interval algebra. Our results are key steps in classifying all $AH$ algebras with the ideal property of no dimension growth.
Strongly continuous one-parameter representations on C*-algebras and their extension to the multiplier algebra are investigated. We give also a proof of the Stone theorem on Hilbert C*-modules and look into some related problems.
We generalise Wigner's theorem to its most general form possible for B(h) in the sense of completely characterising those vector state transformations of B(h) that appear as restrictions of duals of linear operators on B(h). We then use this result to similarly characterise the pure state transformations of general C*-algebras that appear as restrictions of duals of linear operators on the underlying algebras. This result may be interpreted as a noncommutative Banach-Stone theorem.
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