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The seminal 1989 work of Douglas and Paulsen on the theory of Hilbert modules over function algebras precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to blossom, the time has come to collect those results in one volume.
Written by two of the most active and often-cited researchers in the field, Analytic Hilbert Modules offers a clear, logical survey of recent developments, including advances made by authors and others. It provides much-needed insight into function theory of several variables and includes significant results published here for the first time in areas such as characteristic space theory, rigidity phenomena, the equivalence problem, Arveson modules, extension theory, and reproducing Hilbert spaces on n-dimensional complex space.
This book deals with various aspects of commutants and reducing
subspaces of multiplication operators on the Bergman space, along
with relevant von Neumann algebras generated by these operators,
which have been the focus of considerable attention from the
authors and other experts in recent years. The book reviews past
developments and offers insights into cutting-edge developments in
the study of multiplication operators. It also provides commentary
and comparisons to stimulate research in this area.
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