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Page 14
The term scalar will be used for a real or complex number ; a scalar function is a
real or complex valued function . The topology in the ... Let f , g be continuous
scalar functions on a topological space X , and let o be a scalar . Then the
functions ...
The term scalar will be used for a real or complex number ; a scalar function is a
real or complex valued function . The topology in the ... Let f , g be continuous
scalar functions on a topological space X , and let o be a scalar . Then the
functions ...
Page 274
Let S be a compact Hausdorff space and C ( S ) be the algebra of all complex
continuous functions on S . Let A be a closed subalgebra of C ( S ) which
contains the unit e and contains , with f , its complex conjugate f defined by f ( s )
= f ( s ) .
Let S be a compact Hausdorff space and C ( S ) be the algebra of all complex
continuous functions on S . Let A be a closed subalgebra of C ( S ) which
contains the unit e and contains , with f , its complex conjugate f defined by f ( s )
= f ( s ) .
Page 381
10 ] , Hewitt [ 3 ] and Edwards [ 1 ] consider functionals on the space of
continuous functions on a locally compact Hausdorff space which vanish outside
of compact sets . Arens [ 3 ] discussed certain sub - algebras of continuous
functions on a ...
10 ] , Hewitt [ 3 ] and Edwards [ 1 ] consider functionals on the space of
continuous functions on a locally compact Hausdorff space which vanish outside
of compact sets . Arens [ 3 ] discussed certain sub - algebras of continuous
functions on a ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
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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