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A space of pseudoquotients $mathcal{B}(X,S)$ is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and $(x,f) sim (y,g)$ if $gx=fy$. In this note we consider a generalization of this construction where the assumption of commutativity of $S$ by Ore type conditions. As in the commutative case, $X$ can be identified with a subset of $mathcal{B}(X,S)$ and $S$ can be extended to a group $G$ of bijections on $mathcal{B}(X,S)$. We introduce a natural topology on $mathcal{B}(X,S)$ and show that all elements of $G$ are homeomorphisms on $mathcal{B}(X,S)$.
In comparing geodesics induced by different metrics, Audenaert formulated the following determinantal inequality $$det(A^2+|BA|)le det(A^2+AB),$$ where $A, B$ are $ntimes n$ positive semidefinite matrices. We complement his result by proving $$de
By establishing Multiplicative Ergodic Theorem for commutative transformations on a separable infinite dimensional Hilbert space, in this paper, we investigate Pesins entropy formula and SRB measures of a finitely generated random transformations on
We completely characterize the boundedness of the area operators from the Bergman spaces $A^p_alpha(mathbb{B}_ n)$ to the Lebesgue spaces $L^q(mathbb{S}_ n)$ for all $0<p,q<infty$. For the case $n=1$, some partial results were previously obtained by
The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from $RR^n$. The analysis interestingly combines use of Poincar
Let $mathcal{M}$ be a semifinite von Neumann algebra. We equip the associated noncommutative $L_p$-spaces with their natural operator space structure introduced by Pisier via complex interpolation. On the other hand, for $1<p<infty$ let $$L_{p,p}(mat