Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1928
Terminology and Preliminary Notions > The concepts of a Boolean algebra of projections , a spectral measure , an integral with respect to a spectral measure , and so on , which have been explained in Section X.1 , are all fundamental ...
Terminology and Preliminary Notions > The concepts of a Boolean algebra of projections , a spectral measure , an integral with respect to a spectral measure , and so on , which have been explained in Section X.1 , are all fundamental ...
Page 2199
If the strongly closed bounded Boolean algebra B of projections is not complete , there is , by the preceding lemma , a vector x and an increasing generalized sequence { Ex } of projections in B such that the limit lima Eqx does not ...
If the strongly closed bounded Boolean algebra B of projections is not complete , there is , by the preceding lemma , a vector x and an increasing generalized sequence { Ex } of projections in B such that the limit lima Eqx does not ...
Page 2218
Every operator in the weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolution of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of ...
Every operator in the weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolution of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero
Bibliographic information
| Title | Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 Pure and applied mathematics, v. 7 |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | L. Bers, J. J. Stoker |
| Publisher | Wiley-Interscience, 1957 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 667 pages |
| Export Citation | BiBTeX EndNote RefMan |