Abstract

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.
- Well written and lucid presentation.
- Informative and illustrated by examples.
- Familiarizes the reader with the non-normed *-world.

"A distinctive (and very nice) feature of the book is a large number of well-chosen examples. There are also many useful historical remarks...This is a most welcome addition to the existing literature on topological algebras." -MATHEMATICAL REVIEWS

"The author gives a comprehensive account of the theory of topological algebras with involution. A topological algebra is an associative algebra A whose underlying vector space is a topological vector space with the property that the ring multiplication in A is separately continuous. An outstanding class of topological algebras are those equipped with a continuous involution: these are the so-called topological *-algebras. A particular class of topological *-algebras, to which considerable attention is given through the book, is that of m-convex algebras: they are the topological *-algebras whose topology is defined by family of *-preserving submultiplicative seminorms. The whole work is divided into seven chapters.… Special attention is paid to Q-algebras."--ZentralblattMATH