Linear Operators: General theory |
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Page 24
If x € X , there is a sequence of points an € A with an + X . Since { an } is a Cauchy
sequence , and f is uniformly continuous , the sequence { f ( an ) } is also a
Cauchy sequence . Since Y is complete , there is a point g ( x ) € Y with f ( an ) = g
( x ) ...
If x € X , there is a sequence of points an € A with an + X . Since { an } is a Cauchy
sequence , and f is uniformly continuous , the sequence { f ( an ) } is also a
Cauchy sequence . Since Y is complete , there is a point g ( x ) € Y with f ( an ) = g
( x ) ...
Page 145
A sequence of functions { { n } defined on S with values in X converges u -
uniformly if for each ε > 0 there is a set E€ such that v ( u , E ) < ε and such that { In
} converges uniformly on S - E . The sequence { In } converges - uniformly to the ...
A sequence of functions { { n } defined on S with values in X converges u -
uniformly if for each ε > 0 there is a set E€ such that v ( u , E ) < ε and such that { In
} converges uniformly on S - E . The sequence { In } converges - uniformly to the ...
Page 360
which vanishes in a neighborhood of a point p the sequence ( S - 1 ) ( x )
converges to zero uniformly for x in some neighborhood of p . 21 Show that if | Ső
En ( x , z ) dz SM , then the convergence of Snt for a given c . o . n . system is
localized if ...
which vanishes in a neighborhood of a point p the sequence ( S - 1 ) ( x )
converges to zero uniformly for x in some neighborhood of p . 21 Show that if | Ső
En ( x , z ) dz SM , then the convergence of Snt for a given c . o . n . system is
localized if ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive 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 identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero