On completely bounded bimodule maps over W*-algebras

Bojan Magajna

Displaying similar documents to “On completely bounded bimodule maps over W*-algebras”

Factoriality of von Neumann algebras connected with general commutation relations-finite dimensional case

Ilona Królak (2006)

Banach Center Publications

Similarity:

We study a certain class of von Neumann algebras generated by selfadjoint elements $ω_{i} = a_{i} + a ⁺_{i}$ , where $a_{i}, a ⁺_{i}$ satisfy the general commutation relations: $a_{i} a ⁺_{j} = \sum_{r, s} t_{j}^{i} r_{s} a ⁺_{r} a_{s} + δ_{i j} I d$ . We assume that the operator T for which the constants $t_{j}^{i} r_{s}$ are matrix coefficients satisfies the braid relation. Such algebras were investigated in [BSp] and [K] where the positivity of the Fock representation and factoriality in the case of infinite dimensional underlying space were shown. In this paper we prove that under certain conditions on the...

Subharmonicity in von Neumann algebras

Thomas Ransford, Michel Valley (2005)

Studia Mathematica

Similarity:

Let ℳ be a von Neumann algebra with unit $1_{ℳ}$ . Let τ be a faithful, normal, semifinite trace on ℳ. Given x ∈ ℳ, denote by $μ_{t} {(x)}_{t \geq 0}$ the generalized s-numbers of x, defined by $μ_{t} (x)$ = inf||xe||: e is a projection in ℳ i with $τ (1_{ℳ} - e)$ ≤ t (t ≥ 0). We prove that, if D is a complex domain and f:D → ℳ is a holomorphic function, then, for each t ≥ 0, $λ \mapsto \int_{0}^{t} l o g μ_{s} (f (λ)) d s$ is a subharmonic function on D. This generalizes earlier subharmonicity results of White and Aupetit on the singular values of matrices.

A new way to iterate Brzeziński crossed products

Leonard Dăuş, Florin Panaite (2016)

Colloquium Mathematicae

Similarity:

If $A \otimes_{R, σ} V$ and $A \otimes_{P, ν} W$ are two Brzeziński crossed products and Q: W⊗ V → V⊗ W is a linear map satisfying certain properties, we construct a Brzeziński crossed product $A \otimes_{S, θ} (V \otimes W)$ . This construction contains as a particular case the iterated twisted tensor product of algebras.

Biduals of tensor products in operator spaces

Verónica Dimant, Maite Fernández-Unzueta (2015)

Studia Mathematica

Similarity:

We study whether the operator space $V * * \overset{α}{\otimes} W * *$ can be identified with a subspace of the bidual space $(V \overset{α}{\otimes} W) * *$ , for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be...

On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity

J. Chabrowski, Shusen Yan (2002)

Colloquium Mathematicae

Similarity:

We consider the Neumann problem for the equation $- Δ u - λ u = {Q (x) | u |}^{2 * - 2} u$ , u ∈ H¹(Ω), where Q is a positive and continuous coefficient on Ω̅ and λ is a parameter between two consecutive eigenvalues $λ_{k - 1}$ and $λ_{k}$ . Applying a min-max principle based on topological linking we prove the existence of a solution.

On certain functions that generalize von Mangoldt’s function $Λ (n)$

A. Ivić (1975)

Matematički Vesnik

Similarity:

On the Dunford-Pettis property of tensor product spaces

Ioana Ghenciu (2011)

Colloquium Mathematicae

Similarity:

We give sufficient conditions on Banach spaces E and F so that their projective tensor product $E \otimes_{π} F$ and the duals of their projective and injective tensor products do not have the Dunford-Pettis property. We prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T:E* → F** is completely continuous, then $(E \otimes_{ϵ} F) *$ does not have the DPP. We also prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T: F** → E* is...

The order topology for a von Neumann algebra

Emmanuel Chetcuti, Jan Hamhalter, Hans Weber (2015)

Studia Mathematica

Similarity:

The order topology $τ_{o} (P)$ (resp. the sequential order topology $τ_{o s} (P)$ ) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part $M_{s a}$ , the self-adjoint part of the unit ball $M ¹_{s a}$ , and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology...

A minimal regular ring extension of C(X)

M. Henriksen, R. Raphael, R. G. Woods (2002)

Fundamenta Mathematicae

Similarity:

Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,τ). We investigate when G(X) coincides with the ring $C (X, τ_{δ})$ of continuous real-valued functions on the space $(X, τ_{δ})$ , where $τ_{δ}$ is the smallest Tikhonov topology on X for which $τ \subseteq τ_{δ}$ and $C (X, τ_{δ})$ is von Neumann regular. The compact and metric spaces for which $G (X) = C (X, τ_{δ})$ are characterized. Necessary, and different sufficient,...

Noncommutative function theory and unique extensions

David P. Blecher, Louis E. Labuschagne (2007)

Studia Mathematica

Similarity:

We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő $L^{p}$ -distance estimate and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. As a byproduct, this completes the noncommutative analog of the famous cycle of theorems characterizing the function algebraic generalizations of $H^{\infty}$ from the 1960’s. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and...

On the derived tensor product functors for (DF)- and Fréchet spaces

Oğuz Varol (2007)

Studia Mathematica

Similarity:

For a (DF)-space E and a tensor norm α we investigate the derivatives $T o r_{α}^{l} (E, \cdot)$ of the tensor product functor $E \otimes ̃_{α} \cdot : \to$ from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of $T o r ¹_{α} (E, F)$ , which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.

Dual algebras generated by von Neumann n-tuples over strictly pseudoconvex sets

Michael Didas

Similarity:

Let D ⋐ X denote a relatively compact strictly pseudoconvex open subset of a Stein submanifold X ⊂ ℂⁿ and let H be a separable complex Hilbert space. By a von Neumann n-tuple of class over D we mean a commuting n-tuple of operators T ∈ L(H)ⁿ possessing an isometric and weak* continuous $H^{\infty} (D)$ -functional calculus as well as a ∂D-unitary dilation. The aim of this paper is to present an introduction to the structure theory of von Neumann n-tuples of class over D including the necessary function-...

L²-homology and reciprocity for right-angled Coxeter groups

Boris Okun, Richard Scott (2011)

Fundamenta Mathematicae

Similarity:

Let W be a Coxeter group and let μ be an inner product on the group algebra ℝW. We say that μ is admissible if it satisfies the axioms for a Hilbert algebra structure. Any such inner product gives rise to a von Neumann algebra $_{μ}$ containing ℝW. Using these algebras and the corresponding von Neumann dimensions we define $L ²_{μ}$ -Betti numbers and an $L ²_{μ}$ -Euler charactersitic for W. We show that if the Davis complex for W is a generalized homology manifold, then these Betti numbers satisfy a version...

Multiple solutions to a perturbed Neumann problem

Giuseppe Cordaro (2007)

Studia Mathematica

Similarity:

We consider the perturbed Neumann problem ⎧ -Δu + α(x)u = α(x)f(u) + λg(x,u) a.e. in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where Ω is an open bounded set in $ℝ^{N}$ with boundary of class C², $α \in L^{\infty} (Ω)$ with $e s s i n f_{Ω} α > 0$ , f: ℝ → ℝ is a continuous function and g: Ω × ℝ → ℝ, besides being a Carathéodory function, is such that, for some p > N, $s u p_{| s | \leq t} | g (\cdot, s) | \in L^{p} (Ω)$ and $g (\cdot, t) \in L^{\infty} (Ω)$ for all t ∈ ℝ. In this setting, supposing only that the set of global minima of the function $1 / 2 ξ ² - \int_{0}^{ξ} f (t) d t$ has M ≥ 2 bounded connected components, we prove that, for all λ ∈ ℝ small enough,...

Outers for noncommutative $H^{p}$ revisited

David P. Blecher, Louis E. Labuschagne (2013)

Studia Mathematica

Similarity:

We continue our study of outer elements of the noncommutative $H^{p}$ spaces associated with Arveson’s subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in $H^{p}$ actually satisfy the stronger condition that there exist aₙ ∈ A with haₙ...

On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces

Mikio Kato, Lech Maligranda, Yasuji Takahashi (2001)

Studia Mathematica

Similarity:

Some relations between the James (or non-square) constant J(X) and the Jordan-von Neumann constant $C_{N J} (X)$ , and the normal structure coefficient N(X) of Banach spaces X are investigated. Relations between J(X) and J(X*) are given as an answer to a problem of Gao and Lau [16]. Connections between $C_{N J} (X)$ and J(X) are also shown. The normal structure coefficient of a Banach space is estimated by the $C_{N J} (X)$ -constant, which implies that a Banach space with $C_{N J} (X)$ -constant less than 5/4 has the fixed point property. ...

$C^{*}$ algebras associated with von Neumann algebras

Tullio G. Ceccherini-Silberstein (1999)

Bollettino dell'Unione Matematica Italiana

Similarity:

Ad un'algebra di von Neumann separabile $M$ , in forma standard su di uno spazio di Hilbert $H$ , si associa la $C^{*}$ algebra $O_{M}$ definita come la $C^{*}$ algebra $O_{U (M)}$ costituita dai punti fissi dell'algebra di Cuntz generalizzata $O_{H}$ mediante l'azione canonica del gruppo $U (M)$ degli unitari di $M$ . Si dà una caratterizzazione di $O_{M}$ nel caso in cui $M$ è un fattore iniettivo. In seguito, come applicazione della teoria dei sistemi asintoticamente abeliani, si mostra che, se $ω$ è uno stato vettoriale normale e fedele...

Infinitely many positive solutions for the Neumann problem involving the p-Laplacian

Giovanni Anello, Giuseppe Cordaro (2003)

Colloquium Mathematicae

Similarity:

We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ $- Δ_{p} u + λ (x) {| u |}^{p - 2} u = μ f (x, u)$ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, $λ \in L^{\infty} (Ω)$ with $e s s i n f_{x \in Ω} λ (x) > 0$ and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.

Automorphisms of central extensions of type I von Neumann algebras

Sergio Albeverio, Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov (2011)

Studia Mathematica

Similarity:

Given a von Neumann algebra M we consider its central extension E(M). For type I von Neumann algebras, E(M) coincides with the algebra LS(M) of all locally measurable operators affiliated with M. In this case we show that an arbitrary automorphism T of E(M) can be decomposed as $T = T_{a} \circ T_{ϕ}$ , where $T_{a} (x) = a x a^{- 1}$ is an inner automorphism implemented by an element a ∈ E(M), and $T_{ϕ}$ is a special automorphism generated by an automorphism ϕ of the center of E(M). In particular if M is of type $I_{\infty}$ then every band preserving...

Smooth operators in the commutant of a contraction

Pascale Vitse (2003)

Studia Mathematica

Similarity:

For a completely non-unitary contraction T, some necessary (and, in certain cases, sufficient) conditions are found for the range of the $H^{\infty}$ calculus, $H^{\infty} (T)$ , and the commutant, T’, to contain non-zero compact operators, and for the finite rank operators of T’ to be dense in the set of compact operators of T’. A sufficient condition is given for T’ to contain non-zero operators from the Schatten-von Neumann classes $S_{p}$ .

Invariant subspaces for operators in a general II1-factor

Uffe Haagerup, Hanne Schultz (2009)

Publications Mathématiques de l'IHÉS

Similarity:

Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace $𝒦 = 𝒦_{T} (B)$ affiliated with ℳ, such that the Brown measure of ${T |}_{𝒦}$ is concentrated...

A Study on $φ$ -recurrence $τ$ -curvature tensor in $(k, μ)$ -contact metric manifolds

Gurupadavva Ingalahalli, C.S. Bagewadi (2018)

Communications in Mathematics

Similarity:

In this paper we study $φ$ -recurrence $τ$ -curvature tensor in $(k, μ)$ -contact metric manifolds.

Three solutions for a nonlinear Neumann boundary value problem

Najib Tsouli, Omar Chakrone, Omar Darhouche, Mostafa Rahmani (2014)

Applicationes Mathematicae

Similarity:

The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the p(x)-Laplacian of the form $- Δ_{p (x)} u + a (x) | u^{| p (x) - 2} u = μ g (x, u)$ in Ω, ${| \nabla u |}^{p (x) - 2} \partial u / \partial ν = λ f (x, u)$ on ∂Ω. Our technical approach is based on the three critical points theorem due to Ricceri.

The $L^{p}$ -Helmholtz projection in finite cylinders

Tobias Nau (2015)

Czechoslovak Mathematical Journal

Similarity:

In this article we prove for $1 < p < \infty$ the existence of the $L^{p}$ -Helmholtz projection in finite cylinders $Ω$ . More precisely, $Ω$ is considered to be given as the Cartesian product of a cube and a bounded domain $V$ having $C^{1}$ -boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in $Ω$ is solved, which implies existence and a representation of the $L^{p}$ -Helmholtz projection...

Classical boundary value problems for integrable temperatures in a $C^{1}$ domain

Anna Grimaldi Piro, Francesco Ragnedda (1991)

Annales Polonici Mathematici

Similarity:

Abstract. We study a Neumann problem for the heat equation in a cylindrical domain with $C^{1}$ -base and data in $h_{c}^{1}$ , a subspace of $L$ 1. We derive our results, considering the action of an adjoint operator on $B_{T} M O C$ , a predual of $h_{c}^{1}$ , and using known properties of this last space.