منابع مشابه
The Heat Flow of the Ccr Algebra
Let Pf(x) = −if ′(x) and Qf(x) = xf(x) be the canonical operators acting on an appropriate common dense domain in L2(R). The derivations DP (A) = i(PA−AP ) and DQ(A) = i(QA−AQ) act on the ∗-algebra A of all integral operators having smooth kernels of compact support, for example, and one may consider the noncommutative “Laplacian” L = D2 P + D 2 Q as a linear mapping of A into itself. L generat...
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We calculate the real rank and stable rank of CCR algebras which either have only finite dimensional irreducible representations or have finite topological dimension. We show that either rank of A is determined in a good way by the ranks of an ideal I and the quotient A/I in four cases: When A is CCR; when I has only finite dimensional irreducible representations; when I is separable, of genera...
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For a row finite directed graph E, Kumjian, Pask, and Rae-burn proved that there exists a universal C *-algebra C * (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density problems of invertible elements in graph C *-algebras C * (E), and it is proved that C * (E) has stable rank one, that is, the set of all invertible elements is dense in C * (E) (or in its unitization...
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Let A be a unital separable simple infinite dimensional C∗-algebra with tracial rank no 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 ǫ > 0, there exists a selfadjoint element h ∈ As.a such that ‖u− exp(ih)‖ < ǫ. We also study the problem when u c...
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It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the C*-algebra numerical range.
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ژورنال
عنوان ژورنال: Kyungpook mathematical journal
سال: 2008
ISSN: 1225-6951
DOI: 10.5666/kmj.2008.48.2.223