Pseudo-Differential Operators and Differential Structures--II
Copyright policy )Pseudo-Differential Operators and Differential Structures--II
[Part I cf. Contemp. Math. 10, 99-128 (1982; Zbl 0495.58027.] Let \(\bar {\mathcal P}_ 0\) be a closure in the operator norm of an algebra of \(0^{th}\)-order pseudo-differential operators on the differentiable closed manifold M. A link between \(\bar {\mathcal P}_ 0\) and differential structure of M is discussed. In particular, it is constructed an example of a manifold with two distinct differential structures whose associated algebras are distinct, too. Applications to the index theory are discussed too.
pseudo-differential operators, Pseudodifferential and Fourier integral operators on manifolds, Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.), Differentiable structures in differential topology, Index theory and related fixed-point theorems on manifolds, algebra, Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.), differential structure
pseudo-differential operators, Pseudodifferential and Fourier integral operators on manifolds, Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.), Differentiable structures in differential topology, Index theory and related fixed-point theorems on manifolds, algebra, Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.), differential structure
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