Universal Jensen’s Equations in Banach Modules over a C*–Algebra and Its Unitary Group

2004 ◽  
Vol 20 (6) ◽  
pp. 1047-1056 ◽  
Author(s):  
Chun Gil Park
Keyword(s):  
Unitary Group ◽  
C Algebra ◽  
Banach Modules

scholarly journals GENERALIZED JENSEN’S EQUATIONS IN BANACH MODULES OVER A C∗-ALGEBRA AND ITS UNITARY GROUP

2003 ◽  
Vol 7 (4) ◽  
pp. 641-655 ◽  
Author(s):  
Deok-Hoon Boo ◽  
Sei-Qwon Oh ◽  
Chun-Gil Park ◽  
Jae-Myung Park
Keyword(s):  
Unitary Group ◽  
C Algebra ◽  
Banach Modules

THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C*-ALGEBRA

2003 ◽  
Vol 24 (01) ◽  
pp. 115-122
Author(s):  
XIAOCHUN FANG
Keyword(s):  
Unitary Group ◽  
C Algebra ◽  
Trace Space

scholarly journals ON A GENERALIZED TRIF'S MAPPING IN BANACH MODULES OVER A C*-ALGEBRA

2006 ◽  
Vol 43 (2) ◽  
pp. 323-356 ◽  
Author(s):  
Chun-Gil Park ◽  
Themistocles M. Rassias
Keyword(s):  
C Algebra ◽  
Banach Modules

scholarly journals Klein's programme and quantum mechanics

2015 ◽  
Vol 12 (06) ◽  
pp. 1560006
Author(s):  
Jesús Clemente-Gallardo ◽  
Giuseppe Marmo
Keyword(s):  
Quantum Mechanics ◽  
Linear Group ◽  
Unitary Group ◽  
General Linear Group ◽  
Open Quantum Systems ◽  
Compact Subgroup ◽  
Quantum Systems ◽  
General Linear ◽  
C Algebra ◽  
Open Quantum

We review the geometrical formulation of quantum mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of Kraus maps contains, as a maximal subgroup, the general linear group. The same group emerges as the exponentiation of the C*-algebra associated with the quantum system, when thought of as a Lie algebra. Thus, open quantum systems seem to identify the general linear group as associated with quantum mechanics and moreover suggest to extend the Klein programme also to groupoids. The usual unitary group emerges as a maximal compact subgroup of the general linear group.

scholarly journals UNITARIES IN A SIMPLE C*-ALGEBRA OF TRACIAL RANK ONE

2010 ◽  
Vol 21 (10) ◽  
pp. 1267-1281 ◽  
Author(s):  
HUAXIN LIN
Keyword(s):  
State Space ◽  
Unitary Group ◽  
Affine Function ◽  
Connected Component ◽  
Finite Spectrum ◽  
C Algebra ◽  
Infinite Dimensional ◽  
Tracial State ◽  
Rank One ◽  
Tracial Rank

Let A be a unital separable simple infinite dimensional C*-algebra with tracial rank not more than one and with the tracial state space T(A) and let U(A) be the unitary group of A. Suppose that u ∈ U0(A), the connected component of U(A) containing the identity. We show that, for any ϵ > 0, there exists a self-adjoint element h ∈ As.a such that [Formula: see text] We also study the problem when u can be approximated by unitaries in A with finite spectrum. Denote by CU(A) the closure of the subgroup of unitary group of U(A) generated by its commutators. It is known that CU(A) ⊂ U0(A). Denote by [Formula: see text] the affine function on T(A) defined by [Formula: see text]. We show that u can be approximated by unitaries in A with finite spectrum if and only if u ∈ CU(A) and [Formula: see text] for all n ≥ 1. Examples are given for which there are unitaries in CU(A) which cannot be approximated by unitaries with finite spectrum. Significantly these results are obtained in the absence of amenability.

scholarly journals Multilinear Jensen Type Mappings in Banach Modules over a C^✻-Algebra

2005 ◽  
pp. 487-496
Author(s):  
Chun-Gil Park ◽  
Won-Gil Park ◽  
Sang-Hyuk Lee
Keyword(s):  
C Algebra ◽  
Banach Modules
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