Topological algebras with involution [electronic resource] / Maria Fragoulopoulou.

By: Fragoulopoulou, MariaMaterial type: Text

TextSeries: North-Holland mathematics studies ; 200.Publication details: Amsterdam ; Boston : Elsevier, 2005. Edition: 1st edDescription: 1 online resource (xvi, 495 p.)ISBN: 9780444520258; 0444520252; 0080461220 (electronic bk.); 9780080461229 (electronic bk.)Subject(s): Topological algebras | MATHEMATICS -- Algebra -- Linear | Topological algebrasGenre/Form: Electronic books.Additional physical formats: Print version:: Topological algebras with involution.DDC classification: 512/.55 LOC classification: QA326 | .F72 2005ebOnline resources: ScienceDirect | Volltext

Contents:

Introduction. -- 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. -- Bibliography.

Summary: 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.

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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.