Linear Operators: Spectral theory |
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Page 970
... then Xef is in Ly ( R ) L2 ( R ) and f is the limit in the norm of L2 ( R ) of the
generalized sequence { Xef } . Hence , by Theorem 9 , tf is the limit in the norm of
L2 ( M ) of the generalized sequence { t ( Xef ) } . Equivalently , we write tf lim [ e ,
• ] f ...
... then Xef is in Ly ( R ) L2 ( R ) and f is the limit in the norm of L2 ( R ) of the
generalized sequence { Xef } . Hence , by Theorem 9 , tf is the limit in the norm of
L2 ( M ) of the generalized sequence { t ( Xef ) } . Equivalently , we write tf lim [ e ,
• ] f ...
Page 1124
That is , Q ( E ) = Q ( E ) implies E = E. Similarly , y ( E ) SQ ( E ) implies ESE . If En
, E are in F and q ( En ) increases to the limit ( E ) , then it follows from what we
have already proved that En is an increasing sequence of projections and En > E
.
That is , Q ( E ) = Q ( E ) implies E = E. Similarly , y ( E ) SQ ( E ) implies ESE . If En
, E are in F and q ( En ) increases to the limit ( E ) , then it follows from what we
have already proved that En is an increasing sequence of projections and En > E
.
Page 1699
by Lemma 3.22 , defe is the limit in the norm of H ( P ) ( L ) of a sequence { gj } of
functions in CO ( L ) . Putting g , ( x ) = 0 for x in CE - L , it follows from Definition
3.15 that PeF , is the limit in the norm of H ( P ) ( Ce ) of the sequence { g ; } of ...
by Lemma 3.22 , defe is the limit in the norm of H ( P ) ( L ) of a sequence { gj } of
functions in CO ( L ) . Putting g , ( x ) = 0 for x in CE - L , it follows from Definition
3.15 that PeF , is the limit in the norm of H ( P ) ( Ce ) of the sequence { g ; } of ...
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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 |