Linear Operators: General theory |
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Page 747
Math . Soc . 69 , 276 – 291 ( 1950 ) . 9 . Operations in Banach spaces . Trans .
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11 . Strict convexity and smoothness of normed spaces . Trans . Amer . Math .
Math . Soc . 69 , 276 – 291 ( 1950 ) . 9 . Operations in Banach spaces . Trans .
Amer . Math . Soc . 51 , 583 - 608 ( 1942 ) . ... Math . Soc . 51 , 899 – 412 ( 1942 ) .
11 . Strict convexity and smoothness of normed spaces . Trans . Amer . Math .
Page 790
Duke Math . J . 5 , 520 – 534 ( 1939 ) . 2 . On the supporting - plane property of a
convex body . Bull . Amer . Math . Soc . 46 , 482 - 489 ( 1940 ) . Munroe , M . E . 1
. Absolute and unconditional convergence in Banach spaces . Duke Math .
Duke Math . J . 5 , 520 – 534 ( 1939 ) . 2 . On the supporting - plane property of a
convex body . Bull . Amer . Math . Soc . 46 , 482 - 489 ( 1940 ) . Munroe , M . E . 1
. Absolute and unconditional convergence in Banach spaces . Duke Math .
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J . Math . 73 , 357 - 362 ( 1951 ) . 2 . On commutators of bounded matrices . Amer
. J . Math . 73 , 127 - 131 ( 1951 ) . 3 . On the spectra of commutators . Proc . Amer
. Math . Soc . 5 , 929 - 931 ( 1954 ) . 4 . An application of spectral theory to a ...
J . Math . 73 , 357 - 362 ( 1951 ) . 2 . On commutators of bounded matrices . Amer
. J . Math . 73 , 127 - 131 ( 1951 ) . 3 . On the spectra of commutators . Proc . Amer
. Math . Soc . 5 , 929 - 931 ( 1954 ) . 4 . An application of spectral theory to 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