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124
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 559 (0 self)
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is nonseparable. In fact, I. Farah (private communication) has shown that a Hilbert space of dimension 2ℵ0 has a dense subspace which does not contain any uncountable orthonormal set. A similar example was obtained by Dixmier [Dix53]. p. 89 I.2.4.3(i): Some of the statements on p. 9 can be false if the measure
Sukochev Spectral flow and Dixmier traces
, 2002
"... We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semifinite von Neumann algebra. Our results have several applications. We deduce a formula for the Chern character of an odd L (1,∞)s ..."
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Cited by 24 (7 self)
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We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semifinite von Neumann algebra. Our results have several applications. We deduce a formula for the Chern character of an odd L (1
A NOTE ON NONUNITARISABLE REPRESENTATIONS AND RANDOM FORESTS
, 811
"... Abstract. We establish a connection between Dixmier’s unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is nonunitarisable if its first L 2Betti number is nonzero or if it is finitely generated with nontrivial cost. 1. ..."
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Abstract. We establish a connection between Dixmier’s unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is nonunitarisable if its first L 2Betti number is nonzero or if it is finitely generated with nontrivial cost. 1.
NONUNITARISABLE REPRESENTATIONS AND RANDOM FORESTS
, 811
"... Abstract. We establish a connection between Dixmier’s unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is nonunitarisable if its first L 2Betti number is nonzero or if it is finitely generated with nontrivial cost. Our crit ..."
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Cited by 3 (1 self)
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Abstract. We establish a connection between Dixmier’s unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is nonunitarisable if its first L 2Betti number is nonzero or if it is finitely generated with nontrivial cost. Our
Pseudodifferential operators and regularized traces
, 2009
"... This is a survey on trace constructions on various operator algebras with an emphasis on regularized traces on algebras of pseudodifferential operators. For motivation our point of departure is the classical Hilbert space trace which is the unique semifinite normal trace on the algebra of bounded ..."
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operators on a separable Hilbert space. Dropping the normality assumption leads to the celebrated Dixmier traces. Then we give a leisurely introduction to pseudodifferential operators. The parameter dependent calculus is emphasized and it is shown how this calculus leads naturally to the asymptotic
The Geometry of Bundle Gerbes
, 2000
"... This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2gerbe. The notion of a bundle 2gerbe connection and 2curving are introduced and it is shown that there is a class in H 4 (M; Z) associated to any bundle 2gerbe. i iiStatement of Originali ..."
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Cited by 41 (1 self)
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This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2gerbe. The notion of a bundle 2gerbe connection and 2curving are introduced and it is shown that there is a class in H 4 (M; Z) associated to any bundle 2gerbe. i iiStatement of Originality This thesis contains no material which has been accepted for the award of any other degree or diploma at any other university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. I give consent to this copy of my thesis, when deposited in the University Library, being made available for loan and photocopying.
LIMITS OF GROUPOID C*ALGEBRAS ARISING FROM OPEN COVERS
, 803
"... Abstract. I. Raeburn and J. Taylor have constructed continuoustrace C ∗algebras with a prescribed DixmierDouady class, which also depend on the choice of an open cover of the spectrum. We study the asymptotic behavior of these algebras with respect to certain refinements of the cover and appropri ..."
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Abstract. I. Raeburn and J. Taylor have constructed continuoustrace C ∗algebras with a prescribed DixmierDouady class, which also depend on the choice of an open cover of the spectrum. We study the asymptotic behavior of these algebras with respect to certain refinements of the cover
Results 1  10
of
124