This boo k i s a slightly expanded an d revised version of th e lecture notes fro m
the NSF/CBMS Regiona l Conferenc e hel d in Tempe, Arizon a i n May , 1984, at
which th e thir d autho r wa s th e principal lecturer . I n th e boo k w e hav e trie d t o
summarize some of th e voluminous progress that has been made in the theory of
dual algebra s sinc e th e appearanc e i n 1978 o f Scot t Brown' s pioneerin g paper ,
which clearly showe d th e utility of thi s concept for studying th e structure theory
of bounde d linea r operators on Hilbert space. The aim of th e book i s t o present
an approach for studying (nonselfadjoint) dual algebras that allows one to obtain,
in particular, results on invariant subspaces and dilation theory.
The boo k i s pu t togethe r a s follows . Chapte r I consists o f preliminarie s o f a
general nature concerning dual algebras . Most of Chapter s II, III, IV, and X are
taken fro m [6a] , but Chapter s II I an d VI contai n som e ne w material , especiall y
Theorem 6.3 an d th e results leading up to it. Chapters IV and V are taken fro m
[10], and Chapter VIII comes from [7a] and [6b]. Chapter VIII is a rewrite of part
of [11] and [12a], and Chapter IX is taken from a version of [11a].
We wis h t o acknowledg e ou r indebtednes s t o Constanti n Aposto l an d Bel a
Sz.-Nagy, with whom we obtained many of the results to be found herein, and to
Frank Gilfeather and the other members of the Mathematical Sciences Section of
the Nationa l Scienc e Foundation , whos e suppor t an d encouragemen t hav e con-
tributed greatly to our efforts.
Hari Bercovici
Ann Arbor, Michigan Ciprian FoidS
December 1984 - .
Carl Pearcy
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