论文标题
各向异性的gohberg诱饵，用于伪差的算子Abelian紧凑型组
Anisotropic Gohberg Lemmas for Pseudodifferential Operators on Abelian Compact Groups
论文作者
论文摘要
从经典上讲，Gohberg型引理为在Hilbert空间中作用于紧凑型操作员的合适的假数差算子的距离提供了下限，这是“无限符号的行为”。在本文中，伪差操作员与紧凑的Abelian $ x $相关联，其Pontryagin Dual $ \ wideHat X $发挥了重要作用。 Hörmander-type符号类别并不总是可用；它们将被交叉产品$ c^*$ - 代数所取代，该代数涉及消失的振荡条件，即使在特殊情况下，它也更笼统，即使允许完整的假反相差微积分。此外，控制了与大型操作员理想的距离；紧凑型操作员仅形成特定情况。这涉及双重组的某些压缩的不变闭合子集，或者等效地，$ \ ell^\ infty（\ widehat x）$的不变理想。
Classically, Gohberg-type Lemmas provide lower bounds for the distance of suitable pseudodifferential operators acting in a Hilbert space to the ideal of compact operators, in terms of "the behavior of the symbol at infinity". In this article the pseudodifferential operators are associated to a compact Abelian group $X$ and an important role is played by its Pontryagin dual $\widehat X$. Hörmander-type classes of symbols are not always available; they will be replaced by crossed product $C^*$-algebras involving a vanishing oscillation condition, which anyway is more general even in the particular cases allowing a full pseudodifferential calculus. In addition, the distance to a large class of operator ideals is controlled; the compact operators only form a particular case. This involves invariant closed subsets of certain compactifications of the dual group or, equivalently, invariant ideals of $\ell^\infty(\widehat X)$.
