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The aim o f t h i s t h e s i s i s t o g e n e r a l i z e t h e c l a s s i c a l f l o w under a f u n c t i o n c o n s t r u c t i o n t o n o n a b e l i a n W a l g e b r a s . We o b t a i n e x i s t e n c e and u n i q u e n e s s theorems f o r t h i s g e n e r a l i z a t i o n . As an a p p l i c a t i o n we show t h a t the r e l a t i o n s h i p between a c o n t i n u o u s and a d i s c r e t e d e c o m p o s i t i o n o f a p r o p e r l y i n f i n i t e W a l g e b r a i s t h a t o f g e n e r a l i z e d f l o w under a f u n c t i o n . S i n c e c o n t i n u o u s d e c o m p o s i t i o n s a r e known t o e x i s t f o r any p r o p e r l y i n f i n i t e W a l g e b r a , t h i s l e a d s t o g e n e r a l i z a t i o n s of Connes' r e s u l t s on d i s c r e t e d e c o m p o s i t i o n .

Flow under a function and discrete decomposition of properly infiniteW∗-algebras

Flow under a function and discrete decomposition of properly infiniteW^∗-algebras