By Kehe Zhu

An creation to Operator Algebras is a concise text/reference that specializes in the elemental ends up in operator algebras. effects mentioned comprise Gelfand's illustration of commutative C*-algebras, the GNS development, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) useful calculus for regular operators, and kind decomposition for von Neumann algebras. routines are supplied after every one bankruptcy.

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**Example text**

General Let K lies 'P(fo) (I)) 'Pzo the maximal ideal space of we identify If Zo topology is * D and transform point \037 (I) 'Pzo (I) for every f in A(D). By the in the maximal ideal space of A (D), we have a one-to-one continuous mapping from D onto MA(D)' weak-star Thus 'Pzo' = I(zo) for every polynomial I. This implies dense in A(D). So is onto. Suppose Za \037 Zo in D . Then 'PZOl Since both the linear show that the case, continuity, nonvanishing. ker'P = there exists then for Xo each {I E there the mapping consider) C(K) : 'P(/) in x in K has an the By compactness of each = I in C (K) Xl i= X2 such that is one-to-one. *

In 2 that x E N whenever x EN. For x and y in A the assumption in C. )

We next show that -I> In particular, cP is in the Banach dual Suppose cP EM. there exists a function h E Loo (R, dx) such that) PROOF maps maximal is onto. =