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Quasi-standard c*-algebras and norms of inner derivationsSomerset, Douglas W. B. January 1989 (has links)
In the first half of the thesis a necessary and sufficient condition is given for a separable C*-algebra to be *-isomorphic to a maximal full algebra of cross-sections over a base-space such that the fibre algebras are primitive throughout a dense subset. The condition is that the relation of inseparability for pairs of points in the primitive ideal space should be an open equivalence relation. In the second half of the thesis a characterisation is given of those C*- algebras A for which each self-adjoint inner derivation D(α, A) satisfies ∥D(α, A)∥ = 2 inf {∥α-z∥ : z ∈Z(A), the centre of A}. This time the characterisation is that A should be quasicentral and the relation of inseparability for pairs of points in the primitive ideal space should be an equivalence relation. Those C*-algebras for which every inner derivation satisfies the equation are characterised in a similar way.
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Problems in Lie rings and groupsGroves, Daniel January 2000 (has links)
We construct a Lie relator which is not an identical Lie relator. This is the first known example of a non-identical Lie relator. Next we consider the existence of torsion in outer commutator groups. Let L be a free Lie ring. Suppose that 1 < i ≤ j ≤ 2i and i ≤ k ≤ i + j + 1. We prove that L/[L<sup>j</sup>, L<sup>i</sup>, L<sup>k</sup><./em>] is torsion free. Also, we prove that if 1 < i ≤ j ≤ 2i and j ≤ k ≤ l ≤ i + j then L/[L<sup>j</sup>, L<sup>i</sup>, L<sup>k</sup>, L<sup>l</sup>] is torsion free. We then prove that the analogous groups, namely F/[γ<sub>j</sub>(F),γ<sub>i</sub>(F),γ<sub>k</sub>(F)] and F/[γ<sub>j</sub>(F),γ<sub>i</sub>(F),γ<sub>k</sub>(F),γ<sub>l</sub>(F)] (under the same conditions for i, j, k and i, j, k, l respectively), are residually nilpotent and torsion free. We prove the existence of 2-torsion in the Lie rings L/[L<sup>j</sup>, L<sup>i</sup>, L<sup>k</sup>] when 1 ≤ k < i,j ≤ 5, and thus show that our methods do not work in these cases. Finally, we consider the order of finite groups of exponent 8. For m ≥ 2, we define the function T(m,n) by T(m,1) = m and T(m,k + 1) = m<sup>T(m,k)</sup>. We prove that if G is a finite m-generator group of exponent 8 then |G| ≤ T(m, 7<sup>471</sup>), improving upon the best previously known bound of T(m, 8<sup>88</sup>).
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The Cuntz Semigrop of C(X,A)Tikuisis, Aaron 11 January 2012 (has links)
The Cuntz semigroup is an isomorphism invariant for C*-algebras consisting of a semigroup with a compatible (though not algebraic) ordering. Its construction is similar to that of the Murray-von Neumann semigroup (from which the ordered K_0-group arises by the Grothendieck construction), but using positive elements in place of projections. Both rich in structure and sensitive to subtleties of the C*-algebra, the Cuntz semigroup promises to be a useful tool in the classification program for nuclear C*-algebras. It has already delivered on this promise, particularly in the study of regularity properties and the classification of nonsimple C*-algebras. The first part of this thesis introduces the Cuntz semigroup, highlights structural properties, and outlines some applications.
The main result of this thesis, however, contributes to the understanding of what the Cuntz semigroup looks like for particular examples of (nonsimple) C*-algebras. We consider separable C*-algebras given as the tensor product of a commutative C*-algebra C_0(X) with a simple, approximately subhomogeneous algebra A, under the regularity hypothesis that A is Z-stable. (The Z-stability hypothesis is needed even to describe of the Cuntz semigroup of A.) For these algebras, the Cuntz semigroup is described in terms of the Cuntz semigroup of A and the Murray-von Neumann semigroups of C(K,A) for compact subsets K of X. This result is a marginal improvement over one proven by the author in [Tikuisis, A. "The Cuntz semigroup of continuous functions into certain simple C*-algebras." Internat. J. Math., to appear] (there, A is assumed to be unital), although improvements have been made to the techniques used.
The second part of this thesis provides the basic theory of approximately subhomogeneous algebras, including the important computational concept of recursive subhomogeneous algebras. Theory to handle nonunital approximately subhomogeneous algebras is novel here.
In the third part of this thesis lies the main result. The Cuntz semigroup computation is achieved by defining a Cuntz-equivalence invariant I(.) on the positive elements of the C*-algebra, picking out certain data from a positive element which obviously contribute to determining its Cuntz class. The proof of the main result has two parts: showing that the invariant I(.) is (order-)complete, and describing its range.
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The Cuntz Semigrop of C(X,A)Tikuisis, Aaron 11 January 2012 (has links)
The Cuntz semigroup is an isomorphism invariant for C*-algebras consisting of a semigroup with a compatible (though not algebraic) ordering. Its construction is similar to that of the Murray-von Neumann semigroup (from which the ordered K_0-group arises by the Grothendieck construction), but using positive elements in place of projections. Both rich in structure and sensitive to subtleties of the C*-algebra, the Cuntz semigroup promises to be a useful tool in the classification program for nuclear C*-algebras. It has already delivered on this promise, particularly in the study of regularity properties and the classification of nonsimple C*-algebras. The first part of this thesis introduces the Cuntz semigroup, highlights structural properties, and outlines some applications.
The main result of this thesis, however, contributes to the understanding of what the Cuntz semigroup looks like for particular examples of (nonsimple) C*-algebras. We consider separable C*-algebras given as the tensor product of a commutative C*-algebra C_0(X) with a simple, approximately subhomogeneous algebra A, under the regularity hypothesis that A is Z-stable. (The Z-stability hypothesis is needed even to describe of the Cuntz semigroup of A.) For these algebras, the Cuntz semigroup is described in terms of the Cuntz semigroup of A and the Murray-von Neumann semigroups of C(K,A) for compact subsets K of X. This result is a marginal improvement over one proven by the author in [Tikuisis, A. "The Cuntz semigroup of continuous functions into certain simple C*-algebras." Internat. J. Math., to appear] (there, A is assumed to be unital), although improvements have been made to the techniques used.
The second part of this thesis provides the basic theory of approximately subhomogeneous algebras, including the important computational concept of recursive subhomogeneous algebras. Theory to handle nonunital approximately subhomogeneous algebras is novel here.
In the third part of this thesis lies the main result. The Cuntz semigroup computation is achieved by defining a Cuntz-equivalence invariant I(.) on the positive elements of the C*-algebra, picking out certain data from a positive element which obviously contribute to determining its Cuntz class. The proof of the main result has two parts: showing that the invariant I(.) is (order-)complete, and describing its range.
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Construction of the inverse in a Banach algebra by iterationKovács, Rezsö Lázló. January 1968 (has links)
No description available.
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Generalization of Ky Fan-Amir-Moéz-Horn-Mirsky's result on the eigenvalues and real singular values of a matrixYan, Wen, January 2005 (has links) (PDF)
Thesis (Ph.D.)--Auburn University, 2005. / Abstract. Vita. Includes bibliographic references (ℓ. )
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Algebraic structure of degenerate systems /Grundling, Hendrik. January 1986 (has links) (PDF)
Thesis (Ph. D.)--University of Adelaide, Dept. of Mathematical Physics,1986. / Erratum (14 leaves) in pocket. Includes bibliographical references (leaves 124-128).
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A Z2-graded generalization of Kostant's version of the Bott-Borel-Weil theorem /Dolan, Peter, January 2007 (has links)
Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 130-131). Also available for download via the World Wide Web; free to University of Oregon users.
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Preconditioned iterative methods for highly sparse, nonsymmetric, unstructured linear algebra problems /McQuain, William D., January 1992 (has links)
Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 60-63). Also available via the Internet.
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The QR algorithm for eigenvalue estimation theory and experiments /Feng, Wei, Pate, Thomas H., January 2008 (has links)
Thesis--Auburn University, 2008. / Abstract. Vita. Includes bibliographical references (p. 48).
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