By F. Greenleaf

ISBN-10: 0821850342

ISBN-13: 9780821850343

Those lawsuits consequence from a convention on Banach Algebras and numerous advanced Variables held June 21--24, 1983, to honor Professor Charles E. Rickart upon his retirement from Yale college. Articles current fresh advances in a large spectrum of themes concerning Banach algebras, functionality algebras and countless dimensional holomorphy, parts the place Professor Rickart has made vital contributions. From a study perspective, the articles of J. Esterle and B. Kramm are of specified curiosity. even supposing the subjects during this quantity are assorted, a common wisdom of basic notions showing in Banach algebra idea will suffice for realizing so much articles.

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**Example text**

Un + AI( "') un-I + •.. + II. This function can be extended analytically to all each Ili (~) alII:, with its multiplicity if A E F. The A ("') "n ).. l F. 3, counting a;2 A. (~) are well defined in 1 and they are entire because they can be expressed as symmetric func- tion of the ai (in fact we use Rad~'s extension theorem). not all constant because K is not. So u is not in is exceptional for F. 4. Ea: u for Let if and only if 23 ANALYTIC NULTIVALUED FUNCTIONS This result is the best one because, given arbitrary 2n-1 distinct points, it is possible to construct a finite analytic multivalued function on avoiding these points.

SZ-Nagy and J. Smultjan (see the references in [6]) obtained the fallowing result: analytic function from a domain D of z·E Sp f (~) be an into the algebra of compact oper- t ators on a Banach space, and suppose that A E D for which ~ ~ f(~) let t z Sp f(O). Then the set of all is closed and discrete in with K compact, it is the classical result of F. Riesz. f (~) For D. 0:: For a general B. -Nagy believed that this result is deeper than the previous one. K, f, In fact the three given proofs used extensively the important fact that the projections associated to isolated spectral values of a compact operator are finite-dimensional.

We introduce some notation and state some basic facts. When X is a compact Hausdorff space and Z is ~ or ~. a function algebra A on X means an algebra A(X,Z) over Z of Z-valued continuous functions on X whose algebra operations are the pointwise operations of func- tions on and which separates the points and contains all constant functions. X. A is inverse-closed on on X, (l/f) is in X means that for every A, where a Hanach function algebra ~ II· II lex) =1 for all any non-empty open set Y. x For any function algebra Y as explained above.

### Proceedings of the Conference on Banach Algebras and Several Complex Variables (Contemporary Mathematics) by F. Greenleaf

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