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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 26 for “"von Neumann algebras"”.
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Homology of Group Von Neumann Algebras
… the following conjecture is studied: the group von Neumann algebra N(G) is a flat CG-module if and only if the group G is locally virtually cyclic. This paper proves that if G is locally virtually cyclic, then N(G) is flat as a CG-module. The converse is proved for the class of all elementary …
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Kadison -Singer algebras with applications to von Neumann algebras
<p>I develop the theory of Kadison-Singer algebras, introduced recently by Ge and Yuan. I prove basic structure theorems, construct several new examples and explore connections to other areas of operator algebras. In chapter 1, I survey those aspects of the theory of non-selfadjoint algebras that …
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Gaussian-like von Neumann algebras and noncommutative brownian motion
The $q$-Gaussian von Neumann algebras were first defined and studied by Bo\.{z}ejko and Speicher in connection with noncommutative brownian motion. The main results of the present work is to establish that the $q$-Gaussian von Neumann algebras have the weak* completely contractive approximation …
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Zero Divisors, Group Von Neumann Algebras and Injective Modules
… divisor conjecture in relation to the reduced 𝐶*-algebras and operator norm 𝐶*-algebras. For certain classes of groups we address the zero divisor conjecture by providing an isomorphism between the the reduced 𝐶*-algebra and the operator norm 𝐶*-algebra. We also provide an isomorphism between the …
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Ideals in von Neumann algebras and in associated operator algebras
… a Hilbert space is a specific example of a van Neumann algebra, and the theory of compact operators and the ideal they form admit certain generalisations to van Neumann algebras. One of the characterisations of the ideal of compact operators is that it is the closure of the ideal of finite rank …
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On decompositions and Connes's embedding problem of finite von Neumann algebras
… question of Connes asks whether every finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras. As of yet, algebras verified to satisfy Connes's embedding property belong to just a few special classes (e.g. amenable algebras and free group factors). In this …
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Von Neumann algebras, affiliated operators and representations of the Heisenberg relation
<p>Von Neumann algebras are self-adjoint, strong-operator closed subalgebras (containing the identity operator) of the algebra of all bounded operators on a Hilbert space. Factors are von Neumann algebras whose centers consist of scalar multiples of the identity operator. In this thesis, we study …
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Isometries on symmetric spaces associated with semi-finite von Neumann algebras
… symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing …
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Unitarily invariant norms and tensor products of maximal injective von Neumann subalgebras
… consists of four contributions to the study of von Neumann algebras. In the first part, we set up a representation theorem for unitarily invariant norms on finite factor von Neumann algebras. In the second part, we set up a representation theorem for unitarily invariant norms related to infinite …
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Free entropy dimensions and approximate liftings
… J. Shen, we introduce a new invariant on finite von Neumann algebras that do not necessarily act on separable Hilbert space. We show that this invariant is independent of the generating set, and we obtain a number of results for von Neumann algebras that are not finitely generated.</p><p>In the …
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Free products of operator spaces and free Markov processes
… construction, the free product of preduals of von Neumann algebras agrees with the predual of the free product of von Neumann algebras. This answers a question asked by Effros affirmatively. An example is presented to show that the C*-algebra reduced free product of two C*-algebras may be …
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Operator algebra perspectives on interacting quantum systems
… using the mathematical theory of operator algebras. In the first part of this thesis, we consider how to construct quantum many-body systems from one-particle systems. This problem has a well-established solution - namely, the second quantization (or the Gaussian functor). However, it seems …
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Martingale Convergence Techniques in Noncommutative Integration
… idea that the space of operators affiliated to a von Neumann algebra could be interpreted through the lens of integration theory stretches back to the original works of Murray and von Neumann on "rings of operators", the theory they developed to provide a mathematical framework for quantum …
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Kadison -Singer algebras
… defined a new class of non selfadjoint operator algebras---Kadison-Singer algebras or KS-algebras for simplicity. These algebras combine triangularity, reflexivity and von Neumann algebra property into one consideration. Generally speaking, KS-algebras are reflexive, maximal triangular with …
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Burnside factors, amenability defects and transitive families of projections in factors of type II(1)
… transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory of correspondences. From this investigation we are …
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Jordan homomorphisms and derivations on algebras of measurable operators
… invertibility preserving maps between unital algebras are Jordan homomorphisms. This question is still unanswered, and the progress that has been made has mainly been in the context of Banach algebras, including C*-algebras and von Neumann algebras. Let M be a von Neumann algebra with a …
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Aspects of spectral theory for algebras of measurable operators
… the representation theory of commutative C*- and von Neumann algebras as algebras of bounded continuous or measurable functions. For unbounded operators the corresponding theory leads to algebras of unbounded densely defined operators. The thesis looks at aspects of spectral theory in the …
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RECOVERY AND RECONSTRUCTION IN QUANTUM SYSTEMS
… of previous results that applied to type-I von Neumann algebras in [2]. To deal with quantum field theory, the type of the von Neumann algebras is not restrained here. This induces qualitatively new features and requires extra proving techniques. This results hinge on the construction of …
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MF algebras and a Bishop -Stone -Weierstrass theorem result
… first part, we obtain many new results about MF algebras. First, we continue the work on D. Voiculescu's topological free entropy dimension deltatop (x1, ..., xn) for an n-tuple x&ar; = (x1, ..., xn) of elements in a unital C*-algebra. We also introduce a new invariant that is a C*-algebra analog …
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