Linear Operators: Spectral theory |
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Page 995
If y and f are in L ( R ) and L ( R ) respectively and if f ( m ) = 0 for every m in the
spectral set o ( P ) , then olf * ) contains no isolated points . PROOF . We shall
make an indirect proof by supposing that mo is an isolated point of olf * ) . Since
olf ...
If y and f are in L ( R ) and L ( R ) respectively and if f ( m ) = 0 for every m in the
spectral set o ( P ) , then olf * ) contains no isolated points . PROOF . We shall
make an indirect proof by supposing that mo is an isolated point of olf * ) . Since
olf ...
Page 996
From Lemma 12 ( b ) it is seen that olf * o ) Colo ) and from Lemma 12 ( c ) and
the equation of = Tf it follows that o ( f * ) contains no interior point of o ( q ) .
Hence o ( f * o ) is a closed subset of the boundary of o ( p ) . Since f * q = 0 it
follows ...
From Lemma 12 ( b ) it is seen that olf * o ) Colo ) and from Lemma 12 ( c ) and
the equation of = Tf it follows that o ( f * ) contains no interior point of o ( q ) .
Hence o ( f * o ) is a closed subset of the boundary of o ( p ) . Since f * q = 0 it
follows ...
Page 1397
The method of proof is the following : it will be shown that if the theorem is false ,
then a proper symmetric extension T , of T can be constructed whose domain
properly contains both D ( T ) and the null - space of T * . This readily yields a ...
The method of proof is the following : it will be shown that if the theorem is false ,
then a proper symmetric extension T , of T can be constructed whose domain
properly contains both D ( T ) and the null - space of T * . This readily yields a ...
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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 |