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Embeddings of NonCommutative L_pSpaces into NonCommutative . . .
 GAFA GEOMETRIC AND FUNCTIONAL ANALYSIS
, 2000
"... It will be shown that for 1 < p < 2 the Schatten pclass is isometrically isomorphic to a subspace of the predual of a von Neumann algebra. Similar results hold for noncommutative Lp(N,τ)spaces defined by a finite trace on a finite von Neumann algebra. The embeddings rely on a suitable notion of p ..."
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Cited by 8 (2 self)
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It will be shown that for 1 < p < 2 the Schatten pclass is isometrically isomorphic to a subspace of the predual of a von Neumann algebra. Similar results hold for noncommutative Lp(N,τ)spaces defined by a finite trace on a finite von Neumann algebra. The embeddings rely on a suitable notion of pstable processes in the noncommutative setting.
Noncommutative Riemann integration and singular traces for C ∗  algebras
"... Given a C ∗algebra A with a semicontinuous semifinite trace τ acting on the Hilbert space H, we define the family A R of bounded Riemann measurable elements w.r.t. τ as a suitable closure, à la Dedekind, of A, in analogy with one of the classical characterizations of Riemann measurable functions [1 ..."
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Cited by 4 (4 self)
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Given a C ∗algebra A with a semicontinuous semifinite trace τ acting on the Hilbert space H, we define the family A R of bounded Riemann measurable elements w.r.t. τ as a suitable closure, à la Dedekind, of A, in analogy with one of the classical characterizations of Riemann measurable functions [16], and show that A R is a C ∗algebra, and τ extends to a semicontinuous semifinite trace on A R. Then, unbounded Riemann measurable operators are defined as the closed operators on H which are affiliated to A ′′ and can be approximated in measure by operators in A R, in analogy with improper Riemann integration. Unbounded Riemann measurable operators form a τa.e. bimodule on A R, denoted by AR, and such bimodule contains the functional calculi of selfadjoint elements of A R under unbounded Riemann measurable functions. Besides, τ extends to a bimodule trace on AR. As type II1 singular traces for a semifinite von Neumann algebra M with a normal semifinite faithful (nonatomic) trace τ have been defined as traces on M − Mbimodules of unbounded τmeasurable operators [5], type II1 singular traces for a C ∗algebra A with a semicontinuous semifinite (nonatomic) trace τ are defined here as traces on A − Abimodules of unbounded Riemann measurable operators (in AR) for any faithful representation of A. An application of singular traces for C ∗algebras is contained in [6].
Lipschitz continuity of the absolute value and Riesz projections in symmetric operator spaces
, 1995
"... A principal result of the paper is that if E is a symmetric Banach function space on the positive halfline with the Fatou property then, for all semifinite von Neumann algebras (M; ), the absolute value mapping is Lipschitz continuous on the associated symmetric operator space E(M; ) with Lipsch ..."
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Cited by 4 (0 self)
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A principal result of the paper is that if E is a symmetric Banach function space on the positive halfline with the Fatou property then, for all semifinite von Neumann algebras (M; ), the absolute value mapping is Lipschitz continuous on the associated symmetric operator space E(M; ) with Lipschitz constant depending only on E if and only if E has nontrivial Boyd indices. It follows that if
The Daugavet Property Of C*Algebras And NonCommutative L_pSpaces
, 2000
"... We prove that a C # algebra A or a predual N# of a von Neumann algebra N has the Daugavet property if and only if A (or N) is nonatomic. We also prove a similar (although somewhat weaker) result for noncommutative Lpspaces corresponding to nonatomic von Neumann algebras. ..."
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Cited by 2 (0 self)
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We prove that a C # algebra A or a predual N# of a von Neumann algebra N has the Daugavet property if and only if A (or N) is nonatomic. We also prove a similar (although somewhat weaker) result for noncommutative Lpspaces corresponding to nonatomic von Neumann algebras.
Conjugate Operators for Finite Maximal Subdiagonal Algebras
, 1996
"... Let M be a von Neumann algebra with a faithful normal trace , and let H 1 be a finite, maximal, subdiagonal algebra of M. Fundamental theorems on conjugate functions for weak Dirichlet algebras are shown to be valid for noncommutative H 1 . In particular the conjugation operator is shown t ..."
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Let M be a von Neumann algebra with a faithful normal trace , and let H 1 be a finite, maximal, subdiagonal algebra of M. Fundamental theorems on conjugate functions for weak Dirichlet algebras are shown to be valid for noncommutative H 1 . In particular the conjugation operator is shown to be a bounded linear map from L p (M; ) into L p (M; ) for 1 ! p ! 1, and to be a continuous map from L 1 (M; ) into L 1;1 (M; ). We also obtain that if an operator a is such that jaj log + jaj 2 L 1 (M; ) then its conjugate belongs to L 1 (M; ). Finally, we present some partial extensions of the classical Szego's theorem to the noncommutative setting.
TYPE II NON COMMUTATIVE GEOMETRY.
, 2003
"... Abstract. We define the notion of Connesvon Neumann spectral triple and consider the associated index problem. We compute the analytic ChernConnes character of such a generalized spectral triple and prove the corresponding local formula for its Hochschild class. This formula involves the Dixmier t ..."
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Abstract. We define the notion of Connesvon Neumann spectral triple and consider the associated index problem. We compute the analytic ChernConnes character of such a generalized spectral triple and prove the corresponding local formula for its Hochschild class. This formula involves the Dixmier trace for II∞ von Neumann algebras. In the case of foliations, we identify this Dixmier trace with the corresponding measured Wodzicki residue. Contents