相关论文: On injective tensor powers of $\ell_1$

Let $X=(X(n))_{n \in \mathbb{Z_+}}$ be a standard subproduct system of $C^*$-correspondences over a $C^*$-algebra $\mathcal M.$ Assume $T=(T_n)_{n \in \mathbb{Z_+}}$ to be a pure completely contractive, covariant representation of $X$ on a…

With his Clifford algebra of differential forms, Kaehler's algebra addresses the overlooked manifestation of symmetry in the solutions of exterior systems. In this algebra, solutions with a given symmetry are members of left ideals…

In this paper we study \emph{threefolds isogenous to a product of mixed type} i.e. quotients of a product of three compact Riemann surfaces $C_i$ of genus at least two by the action of a finite group $G$, which is free, but not diagonal. In…

In a recent work, Kai Tang conjectured that any compact Hermitian manifold with non-zero constant mixed curvature must be K\"ahler. He confirmed the conjecture in complex dimension $2$ and for Chern K\"ahler-like manifolds in general…

The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst Potential is considered. The…

We show that several known results about the algebraic K-theory of tensor products of algebras with the C*-algebra of compact operators in Hilbert space remain valid for tensor products with any properly infinite C*-algebra.

The well-known Baker-Campbell-Hausdorff theorem in Lie theory says that the logarithm of a noncommutative product e X e Y can be expressed in terms of iterated commutators of X and Y. This paper provides a gentle introduction t{\'o}…

We compute the \v{C}ech cohomology ring of a countable product of infinite projective spaces, and that of an infinite flag manifold. The method of our first result in fact computes the cohomology ring of a countably infinite product of…

For a smooth manifold $M$ we define the Teichm\"uller space $\cT(M)$ of all Riemannian metrics on $M$ and the Teichm\"uller space $\cT^\epsilon(M)$ of $\epsilon$-pinched negatively curved metrics on $M$, where $0\leq\epsilon\leq\infty$. We…

We formulate and prove an index theorem for loop spaces of compact manifolds in the framework of $KK$-theory. It is a strong candidate for the noncommutative geometrical definition (or the analytic counterpart) of the Witten genus. In order…

Unlike for $\ell_p$, $1<p\leq\infty$, the discrete Ces\`aro operator $C$ does not map $\ell_1$ into itself. We identify precisely those weights $w$ such that $C$ does map $\ell_1(w)$ continuously into itself. For these weights a complete…

Grothendieck's theorem asserts that every continuous linear operator from $\ell_1$ to $\ell_2$ is absolutely $(1,1)$-summing. This kind of result is commonly called coincidence result. In this paper we investigate coincidence results in the…

Any compact spacelike hypersurface immersed in a doubly warped product spacetime $I{}_{h} \times_{\rho} \mathbb{P}$ with nondecreasing warping factor $\rho$ must be a spacelike slice, provided that the mean curvature satisfies…

We show that momentum-space tensor monopoles corresponding to nontrivial vector bundle generalizations, known as bundle gerbes, can be realized in bands of three-dimensional topological matter with nontrivial Hopf invariants. We provide a…

Given any compact Riemann surface $C$, there is a canonical meromorphic 2--form $\widehat\eta$ on $C\times C$, with pole of order two on the diagonal $\Delta\, \subset\, C\times C$, constructed in \cite{cfg}. This meromorphic 2--form…

We establish several results concerning tensor products, q-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the root of unity setting. In the generic case, a Weyl…

Let $G$, $H$ be groups. We denote by $\eta(G,H)$ a certain extension of the non-abelian tensor product $G \otimes H$ by $G \times H$. We prove that if $G$ and $H$ are groups that act compatibly on each other and such that the set of all…

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…

We give several equivalent conditions that characterize the 2+2 warped spacetimes: imposing the existence of a Killing-Yano tensor $A$ subject to complementary algebraic restrictions; in terms of the projector $v$ (or of the canonical…

We show that an enlargeable Riemannian metric on a (possibly nonspin) manifold cannot have uniformly positive scalar curvature. This extends a well-known result of Gromov and Lawson to the nonspin setting. We also prove that every…