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A comment on free group factors

Narutaka Ozawa (2010)

Banach Center Publications

Let M be a finite von Neumann algebra acting on the standard Hilbert space L²(M). We look at the space of those bounded operators on L²(M) that are compact as operators from M into L²(M). The case where M is the free group factor is particularly interesting.

A Note on L-sets

Gero Fendler (2002)

Colloquium Mathematicae

Answering a question of Pisier, posed in [10], we construct an L-set which is not a finite union of translates of free sets.

Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey

Nico Spronk (2010)

Banach Center Publications

Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, L - 1 ( G ) and M(G), in a sense which generalizes the Pontryagin duality theorem on abelian groups. We wish to consider the amenability properties of A(G) and B(G) and compare them to such properties for L - 1 ( G ) and M(G). For us, “amenability properties” refers to amenability, weak amenability, and biflatness, as well as some properties which...

Analytic semigroups on vector valued noncommutative L p -spaces

Cédric Arhancet (2013)

Studia Mathematica

We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ( ( T I d E ) t 0 on the vector valued noncommutative L p -space L p ( M , E ) . Moreover, we give applications to the H ( Σ θ ) functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

Caractérisation Des Espaces 1-Matriciellement Normés

Le Merdy, Christian, Mezrag, Lahcéne (2002)

Serdica Mathematical Journal

Let X be a closed subspace of B(H) for some Hilbert space H. In [9], Pisier introduced Sp [X] (1 ≤ p ≤ +∞) by setting Sp [X] = (S∞ [X] , S1 [X])θ , (where θ =1/p , S∞ [X] = S∞ ⊗min X and S1 [X] = S1 ⊗∧ X) and showed that there are p−matricially normed spaces. In this paper we prove that conversely, if X is a p−matricially normed space with p = 1, then there is an operator structure on X, such that M1,n (X) = S1 [X] where Sn,1 [X] is the finite dimentional version of S1 [X]. For p...

Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare, Parasar Mohanty (2015)

Studia Mathematica

In this paper, we introduce and study the notion of completely bounded Λ p sets ( Λ p c b for short) for compact, non-abelian groups G. We characterize Λ p c b sets in terms of completely bounded L p ( G ) multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are Λ p sets for all p < ∞, but are not Λ p c b for any p ≥ 4. This is done by showing that the space of completely bounded L p ( G ) multipliers...

Contractible quantum Arens-Michael algebras

Nina V. Volosova (2010)

Banach Center Publications

We consider quantum analogues of locally convex spaces in terms of the non-coordinate approach. We introduce the notions of a quantum Arens-Michael algebra and a quantum polynormed module, and also quantum versions of projectivity and contractibility. We prove that a quantum Arens-Michael algebra is contractible if and only if it is completely isomorphic to a Cartesian product of full matrix C*-algebras. Similar results in the framework of traditional (non-quantum) approach are established, at the...

Direct limit of matricially Riesz normed spaces

J. V. Ramani, Anil Kumar Karn, Sunil Yadav (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, the -Riesz norm for ordered -bimodules is introduced and characterized in terms of order theoretic and geometric concepts. Using this notion, -Riesz normed bimodules are introduced and characterized as the inductive limits of matricially Riesz normed spaces.

Direct limit of matrix order unit spaces

J. V. Ramani, Anil K. Karn, Sunil Yadav (2008)

Colloquium Mathematicae

The notion of ℱ-approximate order unit norm for ordered ℱ-bimodules is introduced and characterized in terms of order-theoretic and geometric concepts. Using this notion, we characterize the inductive limit of matrix order unit spaces.

Distances between Hilbertian operator spaces

Seán Dineen, Cristina Radu (2014)

Studia Mathematica

We compute the completely bounded Banach-Mazur distance between different finite-dimensional homogeneous Hilbertian operator spaces.

Ditkin sets in homogeneous spaces

Krishnan Parthasarathy, Nageswaran Shravan Kumar (2011)

Studia Mathematica

Ditkin sets for the Fourier algebra A(G/K), where K is a compact subgroup of a locally compact group G, are studied. The main results discussed are injection theorems, direct image theorems and the relation between Ditkin sets and operator Ditkin sets and, in the compact case, the inverse projection theorem for strong Ditkin sets and the relation between strong Ditkin sets for the Fourier algebra and the Varopoulos algebra. Results on unions of Ditkin sets and on tensor products are also given.

Embeddings of finite-dimensional operator spaces into the second dual

Alvaro Arias, Timur Oikhberg (2007)

Studia Mathematica

We show that, if a a finite-dimensional operator space E is such that X contains E C-completely isomorphically whenever X** contains E completely isometrically, then E is 2 15 C 11 -completely isomorphic to Rₘ ⊕ Cₙ for some n, m ∈ ℕ ∪ 0. The converse is also true: if X** contains Rₘ ⊕ Cₙ λ-completely isomorphically, then X contains Rₘ ⊕ Cₙ (2λ + ε)-completely isomorphically for any ε > 0.

Ergodic Dilation of a Quantum Dynamical System

Carlo Pandiscia (2014)

Confluentes Mathematici

Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.

Group C*-algebras satisfying Kadison's conjecture

Rachid El Harti, Paulo R. Pinto (2011)

Banach Center Publications

We tackle R. V. Kadison’s similarity problem (i.e. any bounded representation of any unital C*-algebra is similar to a *-representation), paying attention to the class of C*-unitarisable groups (those groups G for which the full group C*-algebra C*(G) satisfies Kadison’s problem) and thereby we establish some stability results for Kadison’s problem. Namely, we prove that A m i n B inherits the similarity problem from those of the C*-algebras A and B, provided B is also nuclear. Then we prove that G/Γ is...

Ideals and hereditary subalgebras in operator algebras

Melahat Almus, David P. Blecher, Charles John Read (2012)

Studia Mathematica

This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which...

M-complete approximate identities in operator spaces

A. Arias, H. Rosenthal (2000)

Studia Mathematica

This work introduces the concept of an M-complete approximate identity (M-cai) for a given operator subspace X of an operator space Y. M-cai’s generalize central approximate identities in ideals in C*-algebras, for it is proved that if X admits an M-cai in Y, then X is a complete M-ideal in Y. It is proved, using ’special’ M-cai’s, that if J is a nuclear ideal in a C*-algebra A, then J is completely complemented in Y for any (isomorphically) locally reflexive operator space Y with J ⊂ Y ⊂ A and...

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