Linear Operators: Spectral theory |
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Page 949
On the other hand , it has been seen ( Theorem 2 ) that AP is isometric and
isomorphic with C ( S ) , where S is a compact Abelian group , and also ( Lemma
3 ) that the continuous characters of S are of the form eins . By Theorem 1.6 , the
set of ...
On the other hand , it has been seen ( Theorem 2 ) that AP is isometric and
isomorphic with C ( S ) , where S is a compact Abelian group , and also ( Lemma
3 ) that the continuous characters of S are of the form eins . By Theorem 1.6 , the
set of ...
Page 1037
product clearly converges to zero for 1 = 2x it is readily seen that the function Pi (
T ) is analytic for a # 0 and vanishes only for 2 in o ( T ) . It remains to show that if
a + 0 , then P. ( T ) is continuous in T relative to the Hilbert - Schmidt norm in HS .
product clearly converges to zero for 1 = 2x it is readily seen that the function Pi (
T ) is analytic for a # 0 and vanishes only for 2 in o ( T ) . It remains to show that if
a + 0 , then P. ( T ) is continuous in T relative to the Hilbert - Schmidt norm in HS .
Page 1154
Since it is clear that Σ ( 2 ) Ex £ , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) =
c ( 2x2 ) ( E ) , Εε Σ ( 2 ) , for some constant c independent of E. This condition ( i )
, as is seen from Corollary III.11.6 , is a consequence of the assertion that 2 ( 2 ) ...
Since it is clear that Σ ( 2 ) Ex £ , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) =
c ( 2x2 ) ( E ) , Εε Σ ( 2 ) , for some constant c independent of E. This condition ( i )
, as is seen from Corollary III.11.6 , is a consequence of the assertion that 2 ( 2 ) ...
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Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
57 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 function f 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 satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero
Bibliographic information
| Title | Linear Operators: Spectral theory Part 2 of Linear Operators, Nelson Dunford Volume 2 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, William George Bade Volume 2 of Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral Theory, Jacob T. Schwartz Volume 2; Volume 7 of Pure and applied mathematics : a series of texts and monographs Pure and applied mathematics Volume 7 of R.Courant L.Bers and J.J.Stoker Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Edition | reprint |
| Publisher | Interscience Publishers, 1988 |
| Original from | Pennsylvania State University |
| Digitized | 11 Oct 2011 |
| ISBN | 0470226382, 9780470226384 |
| Length | 1070 pages |
| Export Citation | BiBTeX EndNote RefMan |