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This book is composed of three survey lecture courses and nineteen invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, which was held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The lecture courses are: Subalgebras of Graph C*-algebras, by Stephen Power: An introduction to two classes of non-selfadjoint operator algebras, the generalized analytic Toeplitz algebras associated with the Fock space of a graph and subalgebras of graph C*-algebras; C*-algebras and asymptotic spectral theory, by Bernd Silbermann: Three topics on numerical functional analysis that are the cornerstones in asymptotic spectral theory: stability, fractality and Fredholmness; Toeplitz operator algebras and complex analysis, by Harald Upmeier: A survey concerning Hilbert spaces of holomorphic functions on Hermitian symmetric domains of arbitrary rank and dimension, in relation to operator theory, harmonic analysis and quantization.

Operator theory --- analyse (wiskunde)

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Operator theory and functional analysis have a long tradition, initially being guided by problems from mathematical physics and applied mathematics. Much of the work in Banach spaces from the 1930s onwards resulted from investigating how much real (and complex) variable function theory might be extended to fu- tions taking values in (function) spaces or operators acting in them. Many of the ?rst ideas in geometry, basis theory and the isomorphic theory of Banach spaces have vector measure-theoretic origins and can be credited (amongst others) to N. Dunford, I.M. Gelfand, B.J. Pettis and R.S. Phillips. Somewhat later came the penetratingcontributionsofA.Grothendieck,whichhavepervadedandin?uenced theshapeoffunctionalanalysisandthetheoryofvectormeasures/integrationever since. Today, each of the areas of functional analysis/operator theory, Banach spaces, and vector measures/integration is a strong discipline in its own right. However, it is not always made clear that these areas grew up together as cousins and that they had, and still have, enormous in?uences on one another. One of the aims of this monograph is to reinforce and make transparent precisely this important point.

Operator theory --- analyse (wiskunde)

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Operator theory --- analyse (wiskunde)

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Mathematical analysis --- analyse (wiskunde)

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The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces.

Algebra --- Operator theory --- algebra --- analyse (wiskunde) --- matrices