Generalized B*-Algebras and Applications

“This book deals with the theory of locally convex algebras, in general, and of generalizedB_-algebras (GB_-algebras in short) in particular. It is well written and self-contained.” (Lahbib Oubbi, Mathematical Reviews, November, 2023)“The book has been written by specialists that are actively working in the field. The choice of the presented material has been done with great care. The bibliography contains all classical monographs, all important papers, and most recent ones. The book leads the reader 'smoothly' ... . It will therefore serve as an excellent introduction to this theory for graduate students. It should also provide a valuable reference source for researchers in the field.” (Andrzej Sołtysiak, zbMATH 1498.46001, 2022)

• 1. Introduction.- 2. A Spectral Theory for Locally Convex Algebras.- 3. Generalized B*-Algebras: Functional Representation Theory.- 4. Commutative Generalized B*-Algebras: Functional Calculus and Equivalent Topologies.- 5. Extended C*-Algebras and Extended W*-Algebras.- 6. Generalized B*-Algebras: Unbounded *-Representation Theory.- 7. Applications I: Miscellanea.- 8. Applications II: Tensor Products.