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By K. Barbey, H. König

ISBN-10: 3540082522

ISBN-13: 9783540082521

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Extra info for Abstract Analytic Function Theory And Hardy Algebras

Example text

A function Vu6A. 1 a n d ~Fdo ~ I it s u f f i c e s from H a h n - B a n a c h with and ~IQlqdo ~ I and and c l a i m that Fd6M(~) to show t h a t D q ( F O ) ~ I . B u t we have 1 I = ~(uv) and h e n c e 5) F r o m Q6T. 5 T H E O R E M : exists an m6M(~) Let O6Pos(X,Z which is <

1 - c ) ~ + c ~ ) ( u 2) = = O. QED. Let X={a,b}UT A : = C H o I ( D ) Ix c B ( X , E ) = B ( X ) . nals statement It r e q u i r e s lemma. complex O

And prove , m~ that . Now - ~(u)~vdm in particular and hence so once In particular either Vv6A. from the m~(X)mB(X) m6M(~) in B were some ~£M(~) m6B (u-~(u))m = O Then for each M(~)~cB It Vu6A, follows forces assumption = 0 so t h a t all in B ^ and other then have since this that Thus m B - mB(X)m B = either a6M(~) ~(m+~) ~6Z(A) o r M ( ~ ) V c B ^. o r m 6 B ^. W e 6 A± ~ u d m B - ~ ( u ) ~ d m B = O. more one band. either ~ to be neither = 0 or 6 B, since 6 B nor QED. THEOREM: For ~,~ £ Z(A) tical or mutually singular M(m) v n S ( ~ ) v = { O } ) .

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Abstract Analytic Function Theory And Hardy Algebras by K. Barbey, H. König

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