Linear Operators: General theory |
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Page 511
9 . Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of
the product Poex Yz , where Yv = Y , under the mapping T → P8XTx . Show that
the strong topology of operators in B ( X , Y ) is identical with the usual product ...
9 . Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of
the product Poex Yz , where Yv = Y , under the mapping T → P8XTx . Show that
the strong topology of operators in B ( X , Y ) is identical with the usual product ...
Page 540
Nelson Dunford, Jacob T. Schwartz. operator and the operator mapping into a
weakly complete space X . Weakly compact operators from C [ 0 , 1 ] to X were
treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact operators
with ...
Nelson Dunford, Jacob T. Schwartz. operator and the operator mapping into a
weakly complete space X . Weakly compact operators from C [ 0 , 1 ] to X were
treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact operators
with ...
Page 599
( s ) ) for n = 1 , 2 , . . . , then in € L ( S , E , ) , and lim in exists . n + 00 11 Let X ; be
a closed subspace of a B - space X such that TnX , CX , for each operator Tn in a
sequence { Tm , n = 1 , 2 , . . . } of commuting operators in B ( X ) . Let Un be the ...
( s ) ) for n = 1 , 2 , . . . , then in € L ( S , E , ) , and lim in exists . n + 00 11 Let X ; be
a closed subspace of a B - space X such that TnX , CX , for each operator Tn in a
sequence { Tm , n = 1 , 2 , . . . } of commuting operators in B ( X ) . Let Un be the ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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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