I have continued to work through Murphy http://books.google.com/books?id=emNvQgAACAAJ&dq=gerald+murphy+c*+algebras+and+operator+theory&h

I have finished off my revision of sections 1.2 (The Spectrum and the Spectral Radius) & 1.3 (The Gelfand Representation). Section 1.4 is a new topic for me – Compact and Fredholm Operators. A linear map between Banach spaces is *compact* if is totally bounded. As a corollary, all linear maps on finite dimensional spaces are compact. The transpose has been introduced by Murphy is this chapter, and I have seen that if is compact, then so is . A linear map is *Fredholm* if the and are finite dimensional. In terms of progress, I am on p.25 of 265.

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