Linear Operators: General theory |
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Results 1-3 of 82
Page 61
Nelson Dunford, Jacob T. Schwartz. ( i ) and ( ii ) are satisfied , Lemma 3 shows
that the hypotheses of Theorem 1 . 18 are satisfied . From that theorem it is seen
that Tx exists for each X , and that T is continuous . Thus Lemma 4 shows that T is
...
Nelson Dunford, Jacob T. Schwartz. ( i ) and ( ii ) are satisfied , Lemma 3 shows
that the hypotheses of Theorem 1 . 18 are satisfied . From that theorem it is seen
that Tx exists for each X , and that T is continuous . Thus Lemma 4 shows that T is
...
Page 254
Now since Uge U there is a finite chain of the form given in [ * ] above in which
successive vectors have non - zero scalar products . Thus by forming the chain V
2 , Uq , . . . , Uq ' , Vg , it is seen that ug is equivalent to v g , and thus that vp is in
V ...
Now since Uge U there is a finite chain of the form given in [ * ] above in which
successive vectors have non - zero scalar products . Thus by forming the chain V
2 , Uq , . . . , Uq ' , Vg , it is seen that ug is equivalent to v g , and thus that vp is in
V ...
Page 449
Let B , be the dense subset of the boundary B of A at which there are non - zero
functionals tangent to A . We have seen that ( aA , + ( 1 - a ) A ) B = $ for 0 < a < 1
. Since aA , + ( 1 - a ) A is open , ( aA , + ( 1 - a ) A ) n B = $ for 0 < a < 1 . Let pe A
...
Let B , be the dense subset of the boundary B of A at which there are non - zero
functionals tangent to A . We have seen that ( aA , + ( 1 - a ) A ) B = $ for 0 < a < 1
. Since aA , + ( 1 - a ) A is open , ( aA , + ( 1 - a ) A ) n B = $ for 0 < a < 1 . Let pe 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
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |