Self‐adjoint operators, derivations and automorphisms on C*‐algebras

Two numerical characterizations of commutativity for C*-algebra (acting on the Hilbert space H) were given in [1]; one used the norms of self-adjoint operators in (Theorem 2), and the other the numerical index of (Theorem 3). In both cases the proofs were based on the result of Kaplansky which states that if the only nilpotent operator in is 0, then is commutative ([2] 2.12.21, p. 68). Of course the converse also holds.

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SELF-ADJOINT OPERATORS AFFILIATED TO C*-ALGEBRAS

Reviews in Mathematical Physics ◽

10.1142/s0129055x04001984 ◽

2004 ◽

Vol 16 (02) ◽

pp. 257-280 ◽

Cited By ~ 11

Author(s):

MONDHER DAMAK ◽

VLADIMIR GEORGESCU

Keyword(s):

Wave Propagation ◽

Adjoint Operator ◽

C Algebra ◽

C Algebras ◽

Adjoint Operators

We discuss criteria for the affiliation of a self-adjoint operator to a C*-algebra. We consider in particular the case of graded C*-algebras and we give applications to Hamiltonians describing the motion of dispersive N-body systems and the wave propagation in pluristratified media.

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Unitary orbits of self-adjoint operators in simple Z-stable C⁎-algebras

Journal of Functional Analysis ◽

10.1016/j.jfa.2015.08.019 ◽

2015 ◽

Vol 269 (10) ◽

pp. 3304-3315 ◽

Cited By ~ 2

Author(s):

Bhishan Jacelon ◽

Karen R. Strung ◽

Andrew S. Toms

Keyword(s):

C Algebras ◽

Adjoint Operators

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Closed Convex Hulls of Unitary Orbits in Certain Simple Real Rank Zero C* -algebras

Canadian Journal of Mathematics ◽

10.4153/cjm-2016-045-5 ◽

2017 ◽

Vol 69 (5) ◽

pp. 1109-1142 ◽

Cited By ~ 3

Author(s):

P.W. Ng ◽

P. Skoufranis

Keyword(s):

Upper Bound ◽

Convex Combination ◽

Convex Hulls ◽

Real Rank ◽

Real Rank Zero ◽

Rank Zero ◽

C Algebras ◽

Rank One ◽

Adjoint Operators ◽

Tracial States

AbstractIn this paper, we characterize the closures of convex hulls of unitary orbits of self-adjoint operators in unital, separable, simple C* -algebras with non-trivial tracial simplex, real rank zero, stable rank one, and strict comparison of projections with respect to tracial states. In addition, an upper bound for the number of unitary conjugates in a convex combination needed to approximate a self-adjoint are obtained.

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