Related papers: Decomposition of the tensor product of two Hilbert…

In this paper, we investigate whether the tensor product of two frames, each individually localised with respect to a spectral matrix algebra, is also localised with respect to a suitably chosen tensor product algebra. We provide a partial…

Let R be a commutative Noetherian domain, and let M and N be finitely generated R-modules. We give new criteria for determining when M tensor N has torsion. We also give constructive formulas for producing a module in the isomorphism class…

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

If $b$ is an inner function, then composition with $b$ induces an endomorphism, $\beta$, of $L^\infty(\mathbb{T})$ that leaves $H^\infty(\mathbb{T})$ invariant. We investigate the structure of the endomorphisms of $B(L^2(\mathbb{T}))$ and…

In this article we develop a theory for frames in tensor product of Hilbert spaces. We show that like bases if Y_1, Y_2, \cdot \cdot \cdot, Y_n are frames for H_1,H_2, \cdot \cdot \cdot, H_n, respectively, then…

Classical functional calculus is primarily spectral, capturing eigenvalue information through resolvent methods while largely ignoring nilpotent structure. Building on the projector-nilpotent characterization developed in our companion…

Given a real cubic form f(x,y,z), there is a pseudo-Riemannian metric given by its Hessian matrix, defined on the open subset of R^3 where the Hessian determinant h is non-zero. We determine the full curvature tensor of this metric in terms…

Let $\mathscr E$ be a Hilbert $\mathscr A$-module over a $C^*$-algebra $\mathscr A$. For each positive linear functional $\omega$ on $\mathscr A$, we consider the localization $\mathscr E_\omega$ of $\mathscr E$, which is the completion of…

A parametrization of multipartite separable states in a finite-dimensional Hilbert space is suggested. It is proved to be a diffeomorphism between the set of zero-trace operators and the interior of the set of separable density operators.…

Let $n$ be a fixed positive integer and $h: \{1,2,\ldots,n\} \rightarrow \{1,2,\ldots,n\}$ a Hessenberg function. The main results of this paper are twofold. First, we give a systematic method, depending in a simple manner on the Hessenberg…

We study differential complexes of Kolmogorov-Alexander-Spanier type on metric measure spaces associated with unbounded non-local operators, such as operators of fractional Laplacian type. We define Hilbert complexes, observe invariance…

Motivated by the interplay between quadratic algebras, noncommutative geometry, and operator theory, we introduce the notion of quadratic subproduct systems of Hilbert spaces. Specifically, we study the subproduct systems induced by a…

A Demazure crystal is the basis at $q=0$ of a Demazure module. Demazure crystals play an important role in Schubert calculus because the character of a Demazure crystal in type A is identical to a key polynomial, which is closely related to…

Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of C*-correspondences. We discuss the relation of…

We give very simple proofs of the classical results of Magnus and Hill on the spectral properties of the Hilbert matrix $$ H = \left ( {1 \over i+j+ 1 } \right )_{i,j\geq 0} $$ which defines a bounded linear operator on the sequence space…

Let $\omega_\varphi^k(f,\delta)_{w,L_q}$ be the Ditzian-Totik modulus with weight $w$, $M^k$ be the cone of $k$-monotone functions on $(-1,1)$, i.e., those functions whose $k$th divided differences are nonnegative for all selections of…

We demonstrate that the matrix quantum group $SL_q(2)$ gives rise to nontrivial matrix product operator representations of the Lie group $SL(2)$, providing an explicit characterization of the nontrivial global $SU(2)$ symmetry of the XXZ…

For a standard graded ring $R$ of dimension $\geq 2$ over a perfect field of characteristic $p>0$ and a homogeneous ideal $I$ of finite colength, the HK density function of $R$ with respect to $I$ is a compactly supported continuous…

Let g be an affine Kac-Moody Lie algebra and let $\lambda, \mu$ be two dominant integral weights for g. We prove that under some mild restriction, for any positive root $\beta$, $V(\lambda)\otimes V(\mu)$ contains $V(\lambda+\mu-\beta)$ as…

We prove that the Gelfand-Shilov spaces $S^\beta_\alpha$ are topological algebras under the Moyal star product if and only if $\alpha\ge\beta$. These spaces of test functions can be used in quantum field theory on noncommutative spacetime.…