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Topological Algebras with Involution. North-Holland Mathematics Studies Volume 200

  • ID: 1765114
  • Book
  • July 2005
  • Elsevier Science and Technology
This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common.

Key features:

- Lucid presentation
- Smooth in reading
- Informative
- Illustrated by examples
- Familiarizes the reader with the non-normed *-world
- Encourages the hesitant
- Welcomes new comers.

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Part I: General Theory.
I. Background material.
II. Locally C* -algebras.
III. Representation theory.
IV. Structure space of an m* -convex algebra.
V. Hermitian and symmetric topological *-algebras.
Part II: Applications.
VI. Integral representations. Uniqueness of topology.
VII. Tensor products of topological *-algebras.
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M. Fragoulopoulou Department of Mathematics, University of Athens, Greece.
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