Download e-book for kindle: An Introduction to Operator Algebras by Kehe Zhu

By Kehe Zhu

ISBN-10: 0849378753

ISBN-13: 9780849378751

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

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Extra resources for An Introduction to Operator Algebras

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Therefore, '1' = '1't and q. + y) that h( x) is onto. (t) in dx), (R, r lim a for fi in every L 1 (R, dx), f(x) - e itX dx = ) (eito

Then I) Spectral Supposex is in (so xy)-l, But is commutative. 2. ). The for Mapping Theorem) Spectral Izi < every 29) Thus) Ilxll. If is in A Suppose Note 1 (x). by that closed the THEOREM and I(z) is in analytic Izi < Ilxll, then) == a(/(x)) x in Fix PROOF A let and the elements 1, x, (AI Note A E C - a (I if and only if xy-I == - (x)). ) (A): C (AI A is commutative Ao == aA(/(x)) transform. ) {cp(/(x)) series expansion we have) cp(/(x)) for each {I A E see aAo(x), aAo(/(x)) By power with for an x.

Let) {I E C[O, 1] : I' = A with pointwise operations E C[O, I]} and) 11/11 = 11/1100 + 111'1100. ideal space of A is homeomorphic to [0, 1]. The for A is neither isometric Gelfand transform nor onto. 4 Show that the abstract index group of \302\2431 to Z. 5 Let Bn be the open unit ball in cn and let A(Bn) be the \"ball algebra\" in Bn which can be extendedconconsisting of holomorphic functions unit to the closed ball Bn. It is clear that A( Bn) is a Banach tinuously with the and algebra sup-norm pointwise operations.

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An Introduction to Operator Algebras by Kehe Zhu


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