Related papers: Smooth bimodules and cohomology of II$_1$ factors

We study several classes of Banach bimodules over a II$_1$ factor $M$, endowed with topologies that make them "smooth" with respect to $L^p$-norms implemented by the trace on $M$. Letting $M\subset \B= \B(L^2M)$, and $2\leq p < \infty$, we…

We present a sufficient condition for smoothness of bounded linear operators on Banach spaces for the first time. Let $T, A \in B(\mathbb{X}, \mathbb{Y}),$ where $\mathbb{X}$ is a real Banach space and $\mathbb{Y}$ is a real normed linear…

We define a notion of smooth cohomology for $ C^* $-algebras which admit a faithful trace. We show that if $ \A\subseteq B(\h) $ is a $ C^* $-algebra with a faithful normal trace $ \tau $ on the ultra-weak closure $ \bar{\A} $ of $…

For an operator bimodule $X$ over von Neumann algebras $A\subseteq\bh$ and $B\subseteq\bk$, the space of all completely bounded $A,B$-bimodule maps from $X$ into $\bkh$, is the bimodule dual of $X$. Basic duality theory is developed with a…

The notion of a formally smooth bimodule is introduced and its basic properties are analyzed. In particular it is proven that a $B$-$A$ bimodule $M$ which is a generator left $B$-module is formally smooth if and only if the $M$-Hochschild…

In this paper, we study some cohomlogical properties of Banach algebras. For a Banach algebra $A$ and a Banach $A$-bimodule $B$, we investigate the vanishing of the first Hochschild cohomology groups $H^1(A^n,B^m)$ and $H_{w^*}^1(A^n,B^m)$,…

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the…

We study the relation between module and Hochschild cohomology groups of Banach algebras with a compatible module structure. More precisely, we show that for every commutative Banach $ \mathcal{A} $-$ \mathfrak{A}$-bimodule $ X $ and every…

Let $X$ be a real Banach space with an unconditional basis (e.g., $X=\ell_2$ Hilbert space), $\Omega\subset X$ open, $M\subset\Omega$ a closed split real analytic Banach submanifold of $\Omega$, $E\to M$ a real analytic Banach vector…

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an $M$-ideal in the space of bounded operators, a very smooth operator $T$ attains…

In this article, we will give a characterization of Banach bimodules over $C^*$-algebras of compact operators that arises from operator spaces as well as a characterization of (F)-Banach bundles amongst all (H)-Banach bundles over a…

A topological space $X$ is called $\Cal A$-real compact, if every algebra homomorphism from $\Cal A$ to the reals is an evaluation at some point of $X$, where $\Cal A$ is an algebra of continuous functions. Our main interest lies on…

We prove that the regular von Neumann subalgebras $B$ of the hyperfinite II_1 factor $R$ satisfying the condition $B'\cap R=Z(B)$ are completely classified (up to conjugacy by an automorphism of $R$) by the associated discrete measured…

Considering the deeper reasons of the appearance of a remarkable counterexample by J.~Kaad and M.~Skeide [17] we consider situations in which two Hilbert C*-modules $M \subset N$ with $M^\bot = \{ 0 \}$ over a fixed C*-algebra $A$ of…

We first want to consider the formal deformation of a fibered manifold $P \rightarrow M$ as a (bi-)module or subalgebra, where $M$ has a given differential star product. Consequently we want to find obstructions for the existence of a…

Among other things, we show that the ideal sheaf of a complex Hilbert submanifold of a pseudoconvex open subset of Hilbert space is acyclic over the ambient pseudoconvex open set. We also prove a vanishing theorem for a fairly general class…

We use gauge theoretic and algebraic methods to examine sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the character variety of a finitely generated and presented group. We give…

We give a Riemannian structure to the set $\Sigma$ of positive invertible unitized Hilbert-Schmidt operators, by means of the trace inner product. This metric makes of $\Sigma$ a nonpositively curved, simply connected and metrically…

Let $\cal M$ be a Banach C*-module over a C*-algebra $A$ carrying two $A$-valued inner products $< .,. >_1$, $<.,. >_2$ which induce equivalent to the given one norms on $\cal M$. Then the appropriate unital C*-algebras of adjointable…

We introduce a uniform structure on any Hilbert $C^*$-module $\mathcal N$ and prove the following theorem: suppose, $F:{\mathcal M}\to {\mathcal N}$ is a bounded adjointable morphism of Hilbert $C^*$-modules over $\mathcal A$ and $\mathcal…