Chapter 11 Extension to C*-Algebras of the Stone-Weierstrass Theorem

1977 ◽  
pp. 250-263
Keyword(s):  
Weierstrass Theorem ◽  
C Algebras

scholarly journals Subalgebras of C*-algebras and von Neumann algebras

1984 ◽  
Vol 25 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Charles A. Akemann
Keyword(s):  
Recent Work ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Weierstrass Theorem ◽  
Von Neumann ◽  
Matrix Algebras ◽  
C Algebras ◽  
Weakly Closed

Recent work [2, 6] on subalgebras of matrix algebras leads naturally to the following situation. Let A be a C*-subalgebra of the C*-algebra B andM be a weakly closed *-subalgebra of the von Neumann algebra N. Consider the following Conditions.Condition 1. For every b≠ 0 in B there exists a ∈ A such that O≠ab ∈ A.Condition 2. For every b∈B there exists a ≠ 0 in A such that ab ∈ A.If we replace A by M and B by N in Conditions 1 and 2 we get von Neumann algebra versions which we shall call Condition 1'and Condition 2'. Clearly Condition 1 implies Condition 2, and both conditions suggest that A is some kind of weak ideal of B. This paper explores the extent to which this is true. The paper grew out of the author's attempts [1, 3] to generalize the Stone-Weierstrass theorem to C*-algebras.

DEDEKIND COMPLETIONS OF BOUNDED ARCHIMEDEAN ℓ-ALGEBRAS

2012 ◽  
Vol 12 (01) ◽  
pp. 1250139 ◽  
Author(s):  
GURAM BEZHANISHVILI ◽  
PATRICK J. MORANDI ◽  
BRUCE OLBERDING
Keyword(s):  
Inverse Limit ◽  
Stone Duality ◽  
Weierstrass Theorem ◽  
Hausdorff Spaces ◽  
Dedekind Completion ◽  
C Algebra ◽  
C Algebras ◽  
Baer Rings ◽  
Projective Covers

All algebras considered in this paper are commutative with 1. Let baℓ be the category of bounded Archimedean ℓ-algebras. We investigate Dedekind completions and Dedekind complete algebras in baℓ. We give several characterizations for A ∈ baℓ to be Dedekind complete. Also, given A, B ∈ baℓ, we give several characterizations for B to be the Dedekind completion of A. We prove that unlike general Gelfand-Neumark-Stone duality, the duality for Dedekind complete algebras does not require any form of the Stone–Weierstrass Theorem. We show that taking the Dedekind completion is not functorial, but that it is functorial if we restrict our attention to those A ∈ baℓ that are Baer rings. As a consequence of our results, we give a new characterization of when A ∈ baℓ is a C*-algebra. We also show that A is a C*-algebra if and only if A is the inverse limit of an inverse family of clean C*-algebras. We conclude the paper by discussing how to derive Gleason's theorem about projective compact Hausdorff spaces and projective covers of compact Hausdorff spaces from our results.

Another Weak Stone-Weierstrass Theorem for C*-Algebras

1972 ◽  
Vol 15 (3) ◽  
pp. 355-357 ◽  
Author(s):  
George A. Elliott
Keyword(s):  
Weierstrass Theorem ◽  
Commutative Case ◽  
C Algebras ◽  
Pure States

The purpose of this article is to present a new generalization of the classical Stone-Weierstrass theorem for commutative C*-algebras.Under the assumption that B is a sub-C*-algebra of A separating the pure states of A and zero, Kaplansky has conjectured that B=A [4, p. 246]. He gave a proof for the case that A is postliminary ([4, Theorem 7.2]; see also [2, 11.1.8]). Glimm, Akemann, and Sakai have established the conjecture in the presence of various other additional hypotheses, most of which hold in the commutative case ([3], [1], [7]).

A Stone-Weierstrass Theorem for C∗-Algebras

1960 ◽  
Vol 72 (2) ◽  
pp. 216 ◽  
Author(s):  
James Glimm
Keyword(s):  
Weierstrass Theorem ◽  
C Algebras

Investor-State Dispute Settlement under NAFTA Chapter 11: The Shape of Things to Come?

1998 ◽  
Vol 35 ◽  
pp. 263-290
Author(s):  
J. Anthony VanDuzer
Keyword(s):  
Free Trade Agreement ◽  
Dispute Settlement ◽  
Trade Agreement ◽  
Minimum Standards ◽  
The North ◽  
State Behaviour ◽  
Nafta Chapter 11 ◽  
To Come ◽  
The Right

SummaryRecently, there has been a proliferation of international agreements imposing minimum standards on states in respect of their treatment of foreign investors and allowing investors to initiate dispute settlement proceedings where a state violates these standards. Of greatest significance to Canada is Chapter 11 of the North American Free Trade Agreement, which provides both standards for state behaviour and the right to initiate binding arbitration. Since 1996, four cases have been brought under Chapter 11. This note describes the Chapter 11 process and suggests some of the issues that may arise as it is increasingly resorted to by investors.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory

Preventive Debt Restructuring and the Nigerian Draft Insolvency Legislation: Lessons from a Comparative Perspective

2020 ◽  
Vol 28 (1) ◽  
pp. 66-84
Author(s):  
Sanford U. Mba
Keyword(s):  
European Union ◽  
Economic Crisis ◽  
Final Analysis ◽  
The European Union ◽  
Debt Restructuring ◽  
The Us ◽  
Financially Distressed ◽  
Bankruptcy Code ◽  
Second Chance

Recently, the Nigerian Senate passed the Bankruptcy and Insolvency (Repeal and Re-enactment) Bill. This is no doubt a welcome development following the continued demand by insolvency practitioners, academics and other stakeholders for such legislation. The call has not only been for the enactment of just about any legislation, but (consistent with the economic challenges faced by businesses in the country), one that is favourably disposed to the successful restructuring of financially distressed businesses, allowing them to weather the storm of (impending) insolvency, emerge from it and continue to operate within the economy. This article seeks to situate this draft legislative instrument within the present wave of preventive restructuring ably espoused in the European Union Recommendation on New Approaches to Business Rescue and to Give Entrepreneurs a Second Chance (2014), which itself draws largely from Chapter 11 of the US Bankruptcy Code. The article draws a parallel between the economic crisis that gave rise to the preventive restructuring approach of the Recommendation and the present economic situation in Nigeria; it then examines the chances of such restructuring under the Nigerian draft bankruptcy and insolvency legislation. It argues in the final analysis that the draft legislation does not provide for a prophylactic recourse regime for financially distressed businesses. Consequently, a case is made for such an approach.

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