Banach Lecture 15

This lecture ( lecture15) was given on 9/30/09.

Excepts

A bunch of examples were given about compact operators.  For example, the Voltera operator on L^p(0,1), 1\le p \le \infty defined by Vf(x) = \int_0^x f(t)dt.  The notes have a proof showing V is compact for p \ne 1.

Prop II.2.2 An operator is compact iff its adjoint is compact.

Cor. V is compact on L^1(0,1) (because its adjoint is).

Prop. II.2.3 The range of a compact operator contains no infinite dimensional subspaces.

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