Un $C^{*}$-modulo hilbertiano destro $X$ su una $C^{*}$-algebra $\mathcal{A}$ dotato di uno ${}^{*}$-omomorfismo isometrico $\varphi :\mathcal{A}\to {\mathcal{L}}_{\mathcal{A}}\left(X\right)$ viene qui considerato come un oggetto $X_{\mathcal{A}}$ della $C^{*}$-categoria degli $\mathcal{A}$-moduli Hilbertiani destri. Come in [11], associamo ad esso una $C^{*}$-algebra ${\mathcal{O}}_{X_{\mathcal{A}}}$ contenente $X$ come un «$\mathcal{A}$-bimodulo hilbertiano in ${\mathcal{O}}_{X_{\mathcal{A}}}$». Se $X$ è pieno e proiettivo finito ${\mathcal{O}}_{X_{\mathcal{A}}}$ è la $C^{*}$-algebra $C^{*}\left(X\right)$, la generalizzazione delle algebre di Cuntz-Krieger introdotta da Pimsner [27] (e in un caso particolare da Katayama [31]). Più in generale, $C^{*}\left(X\right)$ è canonicamente...

We study a certain class of von Neumann algebras generated by selfadjoint elements ${\omega }_i=a_i+a{⁺}_i$, where $a_i,a{⁺}_i$ satisfy the general commutation relations: $a_{i}a{⁺}_j={\sum }_{r,s}{t}_j^i{r}_{s}a{⁺}_r{a}_s+{\delta }_{ij}Id$. 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...

Let $\mathrm{\Omega }$ be a bounded open subset of $R^n$, $n>4$, of class $C^2$ . Let $u\in H^2\left(\mathrm{\Omega }\right)$ a solution of elliptic non linear non variational system $$a\left(x,u,Du,H\left(u\right)\right)=b\left(x,u,Du\right)$$ where $a\left(x,u,\mu ,\xi \right)$ and $b\left(x,u,\mu \right)$ are vectors in $R^N$, $N\ge 1$, measurable in $x$, continuous in $\left(u,\mu ,\xi \right)$ and $\left(u,\mu \right)$ respectively. Here, we demonstrate that if $b\left(x,u,\mu \right)$ has limit controlled growth, if $a\left(x,u,\mu ,\xi \right)$ is of class $C^1$ in $\xi$ and satisfies the Campanato condition $\left(A\right)$ and, together with $\frac{\partial a}{\partial \xi }$, certain continuity assumptions, then the vector $Du$ is partially Hölder continuous for every exponent $\alpha <1-\frac{n}{p}$.

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 ${\mu }_t{\left(x\right)}_{t\ge 0}$ the generalized s-numbers of x, defined by ${\mu }_t\left(x\right)$ = inf||xe||: e is a projection in ℳ i with $\tau (1_{ℳ}-e)$ ≤ 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, $\lambda \mapsto {\int }_0^{t}log{\mu }_s\left(f\left(\lambda \right)\right)ds$ is a subharmonic function on D. This generalizes earlier subharmonicity results of White and Aupetit on the singular values of matrices.

Let $H_n$ be the Heisenberg group of dimension $2n+1$. Let ${\mathcal{L}}_1,\mathrm{\dots },{\mathcal{L}}_n$ be the partial sub-Laplacians on $H_n$ and $T$ the central element of the Lie algebra of $H_n$. We prove that the kernel of the operator $m\left({\mathcal{L}}_1,\mathrm{\dots },{\mathcal{L}}_n,-iT\right)$ is in the Schwartz space $S\left(H_n\right)$ if $m\in S\left({\mathbb{R}}^{n+1}\right)$. We prove also that the kernel of the operator $h\left({\mathcal{L}}_1,\mathrm{\dots },{\mathcal{L}}_n\right)$ is in $S\left(H_n\right)$ if $h\in S\left({\mathbb{R}}^n\right)$ and that the kernel of the operator $g\left(\mathcal{L},-iT\right)$ is in $S\left(H_n\right)$ if $g\in S\left({\mathbb{R}}^2\right)$. Here $\mathcal{L}={\mathcal{L}}_1+\mathrm{\dots }+{\mathcal{L}}_n$ is the Kohn-Laplacian on $H_n$.

Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo $$-\text{div}\left(Q^{ϵ}G\left(x,N^{ϵ}\nabla u\right)\right)=f^{ϵ},$$ in un dominio limitato $\mathrm{\Omega }$ dello spazio $n$-dimensionale; $Q^{ϵ}=Q^{ϵ}\left(x\right)$ e $N^{ϵ}=N^{ϵ}\left(x\right)$ sono matrici con coefficenti limitati, $N^{ϵ}$ e è invertibile e la sua matrice inversa $R^{ϵ}$ ha anche coefficenti limitati. La non linearità è dovuta alla funzione $G=G\left(x,\xi \right)$; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul $p$-Laplaciano, $1<p<\mathrm{\infty }$, ed assicurano l'esistenza di...

We attempt to generalize conductor degree's results, known in ${\mathbb{P}}^2$, to the case of 0-dimensional schemes of ${\mathbb{P}}^r$. In the first part of this paper, we consider the problem of characterizing the sequences generators's degrees of the conductor which are compatible with a fixed postulation (or Hilbert function) for a set of points in ${\mathbb{P}}^r$ and we determine the conductor degree of every point in a $r$-partial intersection. In addition, we define the separating degree of a point for a 0-dimensional subscheme...