Linear Operators: General theory

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces Borel bounded called clear closed compact operator complex Consequently constant contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm obtained problem Proc projection PROOF properties proved range representation respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero