Linear Operators: General theory |
From inside the book
Results 1-3 of 69
Page 464
( 3 ) For every | ET , sup . zek Rf ( x ) < 00 ; moreover , each linear functional Ø on
I which satisfies inf R } ( x ) = RD ( 1 ) sup R } ( x ) , ter REK ZEK ter also satisfies 0
( 1 ) = f ( x ) , for some X , € K . ( 4 ) If KL , $ < 0 , 0 a limit ordinal , is a monotone ...
( 3 ) For every | ET , sup . zek Rf ( x ) < 00 ; moreover , each linear functional Ø on
I which satisfies inf R } ( x ) = RD ( 1 ) sup R } ( x ) , ter REK ZEK ter also satisfies 0
( 1 ) = f ( x ) , for some X , € K . ( 4 ) If KL , $ < 0 , 0 a limit ordinal , is a monotone ...
Page 557
Consequently , the product R , of all the factors ( a - hilai in R such that di € O ( T )
, still satisfies R ( T ) = 0 . In the same way , the product R , of all the factors ( 2 - hi
) Bi , where Bi = min ( die v ( 2 : ) ) , satisfies R , ( T ) = 0 . Since any polynomial ...
Consequently , the product R , of all the factors ( a - hilai in R such that di € O ( T )
, still satisfies R ( T ) = 0 . In the same way , the product R , of all the factors ( 2 - hi
) Bi , where Bi = min ( die v ( 2 : ) ) , satisfies R , ( T ) = 0 . Since any polynomial ...
Page 613
... continuous real ( or complex ) function f of the nonnegative real variable t
which satisfies the functional equations f ( 0 ) ... the most general continuous
operator valued functions defined on the range t 20 , which satisfy the equations (
i ) T ( t + ...
... continuous real ( or complex ) function f of the nonnegative real variable t
which satisfies the functional equations f ( 0 ) ... the most general continuous
operator valued functions defined on the range t 20 , which satisfy the equations (
i ) T ( t + ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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