Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 85
Page 1015
If lim Tn = T in the norm of HS it follows from Lemma VII.6.5 that the contour C of
the integral in [ * ] contains o ( T ) for all sufficiently large n . From Corollary VII.6.3
it is seen that , in the norm of HS + , lim [ A , TJ - = [ A , -T ]uniformly for 2 in C.
If lim Tn = T in the norm of HS it follows from Lemma VII.6.5 that the contour C of
the integral in [ * ] contains o ( T ) for all sufficiently large n . From Corollary VII.6.3
it is seen that , in the norm of HS + , lim [ A , TJ - = [ A , -T ]uniformly for 2 in C.
Page 1297
The first norm is the norm of the pair [ 1 , T / ] as an element of the graph of T ( T ) .
Now T ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( Ti ( t ) ) is
complete in the norm I / 1 . Since the two additional terms in Ila are the norm of f
as an ...
The first norm is the norm of the pair [ 1 , T / ] as an element of the graph of T ( T ) .
Now T ( t ) is an adjoint ( Theorem 10 ) ; therefore ( cf. XII.1.6 ) D ( Ti ( t ) ) is
complete in the norm I / 1 . Since the two additional terms in Ila are the norm of f
as an ...
Page 1639
1 + ult ; J , m ) This norm makes each of the spaces listed above into a complete F
- space . If k < oo and I is compact , but not otherwise , the spaces C ' ( I ) and C ( I
) are B - spaces under a norm equivalent to the norm displayed , though not ...
1 + ult ; J , m ) This norm makes each of the spaces listed above into a complete F
- space . If k < oo and I is compact , but not otherwise , the spaces C ' ( I ) and C ( I
) are B - spaces under a norm equivalent to the norm displayed , though not ...
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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 |