相关论文: Geometric interplay between function subspaces and…
In this paper we discuss the problem of decomposition for unbounded $2\times 2$ operator matrices by a pair of complementary invariant graph subspaces. Under mild additional assumptions, we show that such a pair of subspaces decomposes the…
We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of differential operators on regular toric varieties, whose fans…
It is a classic result that the geometry of the total space of a principal bundle with reference to the action of the bundle's structure group is codified in the bundle's operation, a collection of derivations comprising the de Rham…
Let ${T_1,...,T_l}$ be a collection of differential operators with constant coefficients on the torus $\mathbb{T}^n$. Consider the Banach space $X$ of functions $f$ on the torus for which all functions $T_j f$, $j=1,...,l$, are continuous.…
We prove sharp inequalities for determinants of Toeplitz operators and twisted Laplace operators on the two-sphere, generalizing the Moser-Trudinger-Onofri inequality. In particular a sharp version of conjectures of Gillet-Soule and Fang…
We are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of $d$-dimensional manifolds, structured hierarchically so that each $d$-dimensional manifold is contained in the boundary of…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
The paper is a colloquial-style discussion of invariants of algebraic surfaces analogous to the Donaldson polynomials, arising from moduli spaces of ``jumping'' Yang--Mills instantons, or moduli spaces of jumping vector bundles. The…
Let X be a complex Banach space of dimension at least 2, and let S be a multiplicative semigroup of operators on X such that the rank of AB - BA is at most 1 for all pairs {A,B} in S. We prove that S has a non-trivial invariant subspace…
Scalar relative invariants play an important role in the theory of group actions on a manifold as their zero sets are invariant hypersurfaces. Relative invariants are central in many applications, where they often are treated locally since…
We revisit the work of Rieffel and van Daele on pairs of subspaces of a real Hilbert space, while relaxing as much as possible the assumption that all the relevant subspaces are in general positions with respect to each other. We work out,…
We present all NSR superstring and super-D-string actions invariant under a set of prescribed gauge transformations, and characterize completely their global symmetries. In particular we obtain locally supersymmetric Born-Infeld actions on…
In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete…
We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and formulate a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle.…
Operators of multiplication by independent variables on the space of square summable functions over the torus and its Hardy subspace are considered. Invariant subspaces where the operators are compatible are described.
In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a band. In addition, we look into some situations under which,…
Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta(T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial…
In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only if every pair of idempotents with a quasinilpotent commutator has a non-trivial common closed…
Starting from an even definite lattice, we construct a principal circle bundle covered by a certain three-step nilpotent Lie group G. On the base space, which is again a nilmanifold, we then study the Dirac operator twisted by the…
We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yield an invertible operator has infinitely many connected…