Differential Geometry of Generalized Grassmann Manifolds in C*-Algebras 241

Amenability, Completely Bounded projections, Dynamical Systems and Smooth Orbits

“…We point out that some further smoothness properties of similarity orbits of group representations (in particular existence of complex structures on the unitary orbits) are discussed in [Ma90] and [MS95].…”

Differential Algebras with Banach-Algebra Coefficients I: from C*-Algebras to the K-Theory of the Spectral Curve

“…The references [18,21] describe the possible analytic structures of the spaces P (A), Gr(p, A), V (p, A) and Λ, and related objects in some depth. For such spaces we wish to point out that in the Banach manifold and C*-algebra setting there is available related work by other authors, using different techniques, that is applicable to a broad scope of independent problems to those considered here; see for instance [2,6,7,8,13,25,30,31,32,34,41,43] (and the references to related work cited therein). The present authors thus acknowledge an inevitable overlap with certain technical details in this regard.…”

“…Other approaches in the operator-theoretic setting as applied to control theory are studied in [26] and to Lax-Phillips scattering in [4]. The present work could in part be viewed as extensions of the Cowen-Douglas theory [14,31] linking complex analytic/algebraic techniques to operator theory, thus suggesting future developments.This Part I is organized as follows: for the reader's sake we recall the necessary setting and details from [20] and other relevant works in an Appendix §A including our parametrized version of the Krichever correspondence, and proceed from §2 to the construction of the above-described C*-algebras in §3. In §4 we pursue the BDF theory and attach topological objects to the spectral curve and Burchnall-Chaundy ring.The new results we have obtained in this Part I are Theorem 3.…”

“…Other approaches in the operator-theoretic setting as applied to control theory are studied in [26] and to Lax-Phillips scattering in [4]. The present work could in part be viewed as extensions of the Cowen-Douglas theory [14,31] linking complex analytic/algebraic techniques to operator theory, thus suggesting future developments.…”