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 1945
Bounded Spectral Operators in Hilbert Space What is the relationship between
the bounded spectral operators in a Hilbert space H and the bounded normal
operators in H ? The central result in this direction is a theorem of Wermer ...
Bounded Spectral Operators in Hilbert Space What is the relationship between
the bounded spectral operators in a Hilbert space H and the bounded normal
operators in H ? The central result in this direction is a theorem of Wermer ...
Page 2169
Self Adjoint Operators in Hilbert Space It is the purpose of this section to show
how the theory of spectral operators may be applied to yield the classical spectral
theorem in Hilbert space , that is , the theorem asserting that a bounded self ...
Self Adjoint Operators in Hilbert Space It is the purpose of this section to show
how the theory of spectral operators may be applied to yield the classical spectral
theorem in Hilbert space , that is , the theorem asserting that a bounded self ...
Page 2591
8 (2075) definition of, XV.2.5 (1931) in Hilbert space, XVI.5. 18 (2162), XVI.6.3(
2171) polar ... XX.l- .14 (2399) in locally convex spaces, XV.16 (2091) Spectral
resolution, definition of, XV.2. 2 (1930) Spectral set for an operator, XV.2 (1930) ...
8 (2075) definition of, XV.2.5 (1931) in Hilbert space, XVI.5. 18 (2162), XVI.6.3(
2171) polar ... XX.l- .14 (2399) in locally convex spaces, XV.16 (2091) Spectral
resolution, definition of, XV.2. 2 (1930) Spectral set for an operator, XV.2 (1930) ...
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Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
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Common terms and phrases
analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly 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 |