Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |
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Page 1931
Of course it is not clear to begin with that a countably additive resolution of the
identity defined on the Borel sets of the plane is uniquely determined by the
spectral operator T . This is the case , but until it is proved we refer to any such
spectral ...
Of course it is not clear to begin with that a countably additive resolution of the
identity defined on the Borel sets of the plane is uniquely determined by the
spectral operator T . This is the case , but until it is proved we refer to any such
spectral ...
Page 2053
In the examples of Theorems 19 and 21 we did not appeal to the general theory ,
as it was clear from the form of exp tà that T ( t ) o was differentiable for t > 0 and
an arbitrary y in HP . It is even clear that the nth order derivative T ' ( n ) ( t ) exists
...
In the examples of Theorems 19 and 21 we did not appeal to the general theory ,
as it was clear from the form of exp tà that T ( t ) o was differentiable for t > 0 and
an arbitrary y in HP . It is even clear that the nth order derivative T ' ( n ) ( t ) exists
...
Page 2159
It is clear that the union of intervals of constancy is open . ... It is clear from the
second expression for yn that it is closed , and it follows from ( G ) that every point
in y is in one of the sets Yn . Thus , by the Baire category theorem ( cf . 1 . 6 .
It is clear that the union of intervals of constancy is open . ... It is clear from the
second expression for yn that it is closed , and it follows from ( G ) that every point
in y is in one of the sets Yn . Thus , by the Baire category theorem ( cf . 1 . 6 .
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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero
Bibliographic information
| Title | Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 Volume 7 of Pure and applied mathematics |
| Authors | Nelson Dunford, Jacob Theodore Schwartz |
| Publisher | Wiley Interscience, 1963 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |