The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, mainly through the interplay of the elementary parts of the theories of analytic functions, rings, and Banach spaces. Many of the theorems are things of great beauty, simple in statement, surprising in content, and elegant in proof. We believe that some of them deserve to be known by every mathematician. The aim of this book is to give an account of the principal methods and results in the theory of Banach algebras, both commutative and non commutative. It has been necessary to apply certain exclusion principles in order to keep our task within bounds. Certain classes of concrete Banach algebras have a very rich literature, namely C*-algebras, function algebras, and group algebras. We have regarded these highly developed theories as falling outside our scope. We have not entirely avoided them, but have been concerned with their place in the general theory, and have stopped short of developing their special properties. For reasons of space and time we have omitted certain other topics which would quite naturally have been included, in particular the theories of multipliers and of extensions of Banach algebras, and the implications for Banach algebras of some of the standard algebraic conditions on rings.

Complete Normed Algebras (Ergebnisse der Mathematik und ihrer Grenzgebiete)

Science & Math

J Duncan

Mathematics

Springer

My Friend Flora is set in the 'Reachfar' country-the Black Isle in Rossshire-where the narrator, Janet Sandison, spent her childhood and which was the setting for the first of Jane Duncan's enchanting books, My Friends the Miss Boyds. The same marvellous sense of the countryside and its people gives its colour and warmth to the story of Flora 'Bedamned' and her family.  Flore and the other Bedamneds (the bye-name, inherited from Flora's great-grandfather, is strikingly apt) first impinge on Janet's life when, at the age of five, she goes to the village school in Achcraggan in 1915. Jamie Bedamned and his forbears have cast their own special and sinister blight on the countryside for generations-morose, black-browed, independent, ill-favoured craftsmen better suited to the construction of dark, satanic mills than the bridges and buildings of the Highlands. But Flora's bedamnedness is of a more passive nature. When her mother dies, she leaves school to bring up her younger brothers and sisters, including the terrifying Georgie, and to keep house for her curmudgeonly old father.  Janet, George and Tom and, in particular, Janet's young aunt Kate battle to improve the lot of the patient-maddeningly patient-Flora, a natural-born doormat. But in the end it is Flora who turns the tables on her would-be benefactors and is the means of bringing unexpected happiness to the Sandisons of Reachfar.  My Friend Flora is without doubt one of Jane Duncan's finest books.

My Friend Flora

Literature & Fiction

Pan.

The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, mainly through the interplay of the elementary parts of the theories of analytic functions, rings, and Banach spaces. Many of the theorems are things of great beauty, simple in statement, surprising in content, and elegant in proof. We believe that some of them deserve to be known by every mathematician. The aim of this book is to give an account of the principal methods and results in the theory of Banach algebras, both commutative and non­ commutative. It has been necessary to apply certain exclusion principles in order to keep our task within bounds. Certain classes of concrete Banach algebras have a very rich literature, namely C*-algebras, function algebras, and group algebras. We have regarded these highly developed theories as falling outside our scope. We have not entirely avoided them, but have been concerned with their place in the general theory, and have stopped short of developing their special properties. For reasons of space and time we have omitted certain other topics which would quite naturally have been included, in particular the theories of multipliers and of extensions of Banach algebras, and the implications for Banach algebras of some of the standard algebraic conditions on rings.

Complete Normed Algebras (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)

F.F. Bonsall

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Books by J Duncan