Linear Operators, Part 2 |
From inside the book
Results 1-3 of 85
Page 1223
How are we to choose its domain ? A natural first guess is to choose as domain the collection D , of all functions with one continuous derivative . If | and g are any two such functions , we have ( iDf , g ) = Sit ' ( 0 ) 8 ( t ) dt g ...
How are we to choose its domain ? A natural first guess is to choose as domain the collection D , of all functions with one continuous derivative . If | and g are any two such functions , we have ( iDf , g ) = Sit ' ( 0 ) 8 ( t ) dt g ...
Page 1248
The subspace M is called the x ' initial domain of P and PM ( = PH ) is called the final domain of P. 5 LEMMA . ... In this case PP * is also a projection and the ranges of P * P and PP * are the initial and final domains , respectively ...
The subspace M is called the x ' initial domain of P and PM ( = PH ) is called the final domain of P. 5 LEMMA . ... In this case PP * is also a projection and the ranges of P * P and PP * are the initial and final domains , respectively ...
Page 1249
Thus PP * I is a projection whose range is N = PM , the final domain of P. To complete the proof it will suffice to show that P * P is a projection if P is a partial isometry . Let x , v e M , the initial domain of P. Then the identity ...
Thus PP * I is a projection whose range is N = PM , the final domain of P. To complete the proof it will suffice to show that P * P is a projection if P is a partial isometry . Let x , v e M , the initial domain of P. Then the identity ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
13 other sections not shown
Common terms and phrases
additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero