Related papers: A characterization of absolutely dilatable Schur m…

We consider $\mathcal N=2$ $SU(2)$ gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic $\Omega$-deformation. We compute them by equivariant…

The paper is devoted to characterizing convex trace ranges in finite atomic von Neumann algebras. The main result provides us with the necessary and sufficient condition for the range of a faithful normal trace on a finite atomic von…

Let $(\Omega_1, \mathcal{F}_1, \mu_1)$ and $(\Omega_2, \mathcal{F}_2, \mu_2)$ be two measure spaces and let $1 \leq p,q \leq +\infty$. We give a definition of Schur multipliers on $\mathcal{B}(L^p(\Omega_1), L^q(\Omega_2))$ which extends…

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N < 6 or p > 2^N. Let G act rationally on a finitely generated…

A finite von Neumann algebra $\mathcal{M}$ with a faithful normal trace $% \tau $ has Haagerup's approximation property (relative to a von Neumann subalgebra $\mathcal{N}$) if there exists a net $(\phi_{\alpha})_{\alpha\in \Lambda}$ of…

We consider the Aluthge transform $|T|^{1/2}U|T|^{1/2}$ of a Hilbert space operator $T$, where $T=U|T|$ is the polar decomposition of $T$. We prove that the map that sends $T$ to its Aluthge transform is continuous with respect to the norm…

For a given C*-algebra $\mathcal{A}$, we establish the existence of maximal and minimal operator $\mathcal{A}$-system structures on an AOU $\mathcal{A}$-space. In the case $\mathcal{A}$ is a W*-algebra, we provide an abstract…

We investigate conditions for the extendibility of continuous algebra homomorphisms $\phi$ from the Fourier algebra $A(F)$ of a locally compact group $F$ to the Fourier-Stieltjes algebra $B(G)$ of a locally compact group $G$ to maps between…

A linear mapping $\phi$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$, and $\phi$ is called a derivable mapping at…

Let $G$ be a locally compact unimodular group, and let $\phi$ be some function of $n$ variables on $G$. To such a $\phi$, one can associate a multilinear Fourier multiplier, which acts on some $n$-fold product of the non-commutative…

Let $\M$ be a finite von Neumann algebra acting on a Hilbert space $\H$ and $\AA$ be a transitive algebra containing $\M'$. In this paper we prove that if $\AA$ is 2-fold transitive, then $\AA$ is strongly dense in $\B(\H)$. This implies…

We consider the class of integral operators $Q_\f$ on $L^2(\R_+)$ of the form $(Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy$. We discuss necessary and sufficient conditions on $\phi$ to insure that $Q_{\phi}$ is bounded, compact, or in the…

Let $R$ be a semiartinian (von Neumann) regular ring with primitive factors artinian. The dimension sequence $\mathcal D _R$ is an invariant that captures the various skew-fields and dimensions occurring in the layers of the socle sequence…

In the setting of a non-complete doubling metric measure space $(\Omega,d,\mu)$, we construct various bounded linear trace and extension operators for homogeneous and inhomogeneous Besov spaces $B^\alpha_{p,q}$. Equipping the boundary…

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong…

Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a quaternionic normal operator with the domain $\mathcal{D}(T) \subset \mathcal{H}$. Then for a fixed unit imaginary quaternion $m$, there exists a Hilbert basis…

A Lie algebra $L$ of dimension $n \ge1 $ may be classified, looking for restrictions of the size on its second integral homology Lie algebra $H_2(L,\mathbb{Z})$, denoted by $M(L)$ and often called Schur multiplier of $L$. In case $L$ is…

We study Toeplitz operators with respect to a commuting $n$-tuple of bounded operators which satisfies some additional conditions coming from complex geometry. Then we consider a particular such tuple on a function space. The algebra of…

We provide a characterisation of Schur multiplicative maps on both finite and infinite dimensional matrix spaces, and show that every surjective Schur multiplicative contraction is automatically an isometry. We also generalise this result…

We prove that if $\mathcal M$ is a properly infinite von Neumann algebra and $LS(\mathcal M)$ is the local measurable operator algebra affiliated with $\mathcal M$, then every Jordan derivation from $LS(\mathcal M)$ into itself is…