Banach Algebras 97 : Proceedings of the 13th International Conference on Banach Algebras Held at the Heinrich Fabri Institute of the University of Tübingen in Blaubeuren, July 20-August 3, 1997

Since the pioneering works by Gelfand and Rickart in the 1940's, the theory of Banach algebras has evolved into a field which is fundamental for many mathematical disciplines. The Banach algebra structure naturally turns up in Harmonic Analysis, Complex Function Theory, Spectrai Theory of Operators (and hence in Dynamical Systems as well as in Differential Equations), Probability Theory, Numerical Analysis, and, in the disguise of self-adjoint algebras of operators on Hilbert space, has close connections to Quantum Mechanics and Quantum Field Theory. In each of these, the interplay of algebra and analysis is fruitfully exploited. The objective of the 13th in the series of international conferences on Banach algebras was to give an account on the present state of the various aspects of the by now highly-developed theory of Banach algebras and to reflect some of its interrelations with other areas. In addition to talks by the participants, there were eight workshops organised in the afternoons dedicated to more specialised areas of interest. The idea of these workshops was to provide a forum for close interaction among those participants who are particularly knowledgeable and interested in one of these specialised topics. The chairmen and titles of the workshops were W. G. Bade: Algebraic Structure of Banach Algebras Preface Contents Historical Note A history of conferences on Banach algebras Research Articles Commutant algebras for certain differential operators in L p (R) Algebras of smooth functions Sur les transformations qui conservent le spectre Localized L 1 -factorization for absolutely continuous contractions Averaging with virtual diagonals and geometry of representations Second-order cohomology groups of some semigroup algebras Compact elements in weighted discrete semigroup algebras C 00 -representations of H∞(G) with dominating Harte spectrum Embedding semigroups in commutative radical Banach algebras Generalizations of Fredholm operators Oka’s principle for special Fréchet Lie groups and homogeneous manifolds in topological algebras of the microlocal analysis Some concepts from group cohomology in the Banach algebra context Weak amenability of C*-algebras and a theorem of Goldstein The generalized Carleson condition in certain spaces of analytic functions Description of spatially projective operator C*-algebras, and around it Endomorphisms of Banach algebras of infinitely differentiable functions The Browder spectrum through local spectral theory On ⍦*- and C*-algebras of pseudodifferential operators on manifolds with conical singularities Amenable Banach algebras with discrete spectrum Excision in the cohomology of Banach algebras with coefficients in dual bimodules Extending the norm from special Jordan triple systems to their associative envelopes Natural spectrum, natural local spectra, and spectral mapping theorems for multipliers on Banach algebras Invariant subspaces for tuples with normal dilations The structure of contractible and amenable Banach algebras On some properties of the difference spectrum Homological dimensions of tensor products of Banach algebras Derivations which are unbounded on the polynomials Elements in the radical of a Banach algebra obeying the unbounded Kleinecke-Shirokov conjecture Rare sets and derivations of Banach algebras Problems and Solutions Questions on automatic continuity Lifting of idempotent operator functions Various notions of amenability, a survey of problems List of Open Problems List of Contributors and Participants

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

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