theory o r t o predictio n theory , etc . I hav e indicate d th e proble m an d th e mos t interestin g results concernin g unitar y dilation s o f a commutativ e syste m o f contraction s bu t hav e excluded an y referenc e t o dilation s o f representation s o f functio n algebras , o r t o unitar y p-dilations. Thus, i n short , I di d no t endeavou r t o giv e a bird' s ey e vie w o f all th e real m o f operator theor y connecte d wit h th e dilatio n concept instea d I trie d t o give a possibl y clear pictur e o f som e o f it s mai n provinces . I hop e tha t som e o f th e reader s wil l fin d the them e interestin g an d promisin g enoug h fo r furthe r study , wit h th e hel p o f th e boo k [H] an d th e curren t literature . Szeged July 197 3 B " 1 S S 2 - N a g y v m

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