相关论文: On decomposition for pairs of twisted contractions

This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight setting are obtained. As applications, we obtain…

Given a two-dimensional quantum lattice model with an abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a…

In this paper, we completely characterize when two dual truncated Toeplitz operators are essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact. Our main idea is to study dual truncated…

An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with…

Mostow's Decomposition Theorem is a refinement of the polar decomposition. It states the following. Let G be a compact connected semi-simple Lie group with Lie algebra g. Given a subspace h of g such that [X, [X, Y]] belongs to h for all X…

For a Calabi-Yau triangulated category $\mathcal{C}$ of Calabi-Yau dimension $d$ with a $d-$cluster tilting subcategory $\mathcal{T}$, it is proved that the decomposition of $\mathcal{C}$ is determined by the special decomposition of…

An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable. One of the features of this special case is that the corresponding Azumaya bundle…

An operator T on Hilbert space is a 3-isometry if there exists operators B and D such that (T*)^n T^n = I+nB +n^2 D. An operator J is a Jordan operator if it the sum of a unitary U and nilpotent N of order two which commute. If T is a…

We introduce and study Dirichlet-type spaces $\mathcal D(\mu_1, \mu_2)$ of the unit bidisc $\mathbb D^2,$ where $\mu_1, \mu_2$ are finite positive Borel measures on the unit circle. We show that the coordinate functions $z_1$ and $z_2$ are…

In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…

In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…

We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…

We investigate the norm identity $\|uC_\phi + T\| = \|u\|_\infty + \|T\|$ for classes of operators on $C(S)$, where $S$ is a compact Hausdorff space without isolated point, and characterize those weighted composition operators which satisfy…

In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and…

For a contraction P and a bounded commutant S of P, we seek a solution X of the operator equation S-S*P = (I-P*P)^1/2 X(I-P*P) 1/2, where X is a bounded operator on Ran(I-P*P) 1/2 with numerical radius of X being not greater than 1. A pair…

To a continuous action of a vector group on a $C^*$-algebra, twisted by the imaginary exponential of a symplectic form, one associates a Rieffel deformed algebra as well as a twisted crossed product. We show that the second one is…

Let T be a C_{\cdot 0}-contraction on a Hilbert space H and S be a non-trivial closed subspace of H. We prove that S is a T-invariant subspace of H if and only if there exists a Hilbert space D and a partially isometric operator \Pi :…

Three-dimensional N = 4 supersymmetric quantum field theories admit two topological twists, the Rozansky-Witten twist and its mirror. Either twist can be used to define a supersymmetric compactification on a Riemann surface and a corre-…

This note introduces a special class of tuples of bounded operators on a Hilbert space. It is called the Agler Young class. Major results about this class include a Wold decomposition and a dilation theorem. The structure of the dilation is…

This is a study of twisted K-theory on a product space $T \times M$. The twisting comes from a decomposable cup product class which applies the 1-cohomology of $T$ and the 2-cohomology of $M$. In the case of a topological product, we give a…