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Showing 1 to 20 of 23 for “"Von Neumann Algebra"”.
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A Beurling Theorem for Noncommutative Hardy Spaces Associated with a Semifinite von Neumann Algebra with Various Norms
… H-invariant spaces in relation to a semifinite von Neu-mann algebra M with a semifinite, faithful, normal tracial weight τ, using an extension of Arveson’s non-commutative Hardy space H-. First we prove a Beurling-Blecher-Labuschagne theorem for H-invariant subspaces of L p (M,τ) when 0 …
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On the Operator Space UMD Property and Non-Commutative Martingale Inequalities
… BMO,Lp pq = Lq holds in the setting of a finite von Neumann algebra M , equipped with an increasing filtration ( M n)n≥1 of von Neumann subalgebras. We also obtain the corresponding results for the real method of interpolation. We discuss the appropriate operator space matrix norms and show …
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Aspects of duality theory for spaces of measurable operators
It is well known that a commutative von Neumann algebra can be represented as a space of essentially bounded functions over a localizable measure space. In non-commutative integration theory, a von Neumann algebra takes over the role of the space of essentially bounded measurable functions. If the …
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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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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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Quasi-Pure E0-Semigroups
… class of quasi-pure E0-semigroups acting on a von Neumann algebra as that with equal tail and fixed-point algebras and we describe these notable algebras for E0-semigroups of B(H) where H is a separable Hilbert space. We consider the classes of pure, quasi-pure and ergodic E0-semigroups induced …
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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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On the Necessity of Complex Numbers in Quantum Mechanics
… long standing problem that can be traced back to von Neumann’s mathematical formulation of quantum mechanics. However up to now there are no examples of quantum systems described in Hilbert spaces whose scalar field is different from the set of complex numbers. We show that elementary relativistic …
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Εργοδικά θεωρήματα σε von Neumann άλγεβρες και εργοδικά θεωρήματα για τυχαία σύνολα σε χώρους Banach
Let M be von Neumann algebra with a faithful normal semifinite weight and a semigroup of kernels on it. In paragraph 2 maximal ergodic theorems are given for additive and strongly superadditive processes, one dimensional or multidimensional. In paragraph 3 we deal with continuous parameter …
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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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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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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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Properties of Pure Completely Positive Linear Maps of Operator Systems
… operator system spanned in the group C*-algebra C*(Fn) by the n generators of the free group Fn and their inverses, then the identity map in : Sn -> Sn is shown to be a pure completely positive map. Similarly, the identity map jn : NC(n) -> NC(n) on the noncommutative n-cube NC(n) in the …
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Ideals in von Neumann algebras and in associated operator algebras
… topology. These operators form an ideal, in the algebra of all continuous linear operators on the Hilbert space, which is closed in the uniform norm. In the case that the underlying Hilbert space is separable this is the only such ideal, while for non-separable Hilbert spaces the norm-closed …
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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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On approximation properties of group C* - algebras
… of an approximation property for the reduced C*- algebra of a group: the invariant approximation property. This statement captures a particular relationship between three important operator algebras associated with a group: the reduced C*- algebra, the von Neumann algebra, and the uniform Roe …
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Smoothing estimates for non commutative spaces
… further develop a general embedding theory for von Neumann algebra, continuing the work for \cite{junge2010mixed}. Finally we prove the cb version of Varopolous's theorem and provide some examples and applications. The third part of the thesis proves the existence of abstract Strichartz …
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A study of super-KMS functionals
… properties of super-KMS functionals on ℤ₂ graded von Neumann algebras. We prove that if a normal self-adjoint functional ω is weakly super-KMS, then the uniquely defined by the polar decomposition of ω positive functional |ω| is KMS. We construct a graded representation of any von Neumann algebra …
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On p-operator spaces and their applications
… relationship between locally compact groups and algebras associated with them. For example, Johnson proved that a locally compact group G is amenable if and only if the convolution algebra L1(G) is amenable as a Banach algebra, and Ruan showed that G is amenable if and only if the Fourier algebra …
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