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 1967
If a B * -subalgebra X of a B * -algebra Y has the same unit e as y , then an element in X with an inverse in Y has this inverse also in X. PROOF . We first show that e = e * . Since e is the unit , e * = ee * , and so e = ee * = ( ee ...
If a B * -subalgebra X of a B * -algebra Y has the same unit e as y , then an element in X with an inverse in Y has this inverse also in X. PROOF . We first show that e = e * . Since e is the unit , e * = ee * , and so e = ee * = ( ee ...
Page 2065
Since , for a in Aį , the function â is continuous on the compact space S , it follows that an operator a in A , has an inverse in A if à ( s ) does not vanish on S. A celebrated theorem of N. Wiener gives more by asserting that the ...
Since , for a in Aį , the function â is continuous on the compact space S , it follows that an operator a in A , has an inverse in A if à ( s ) does not vanish on S. A celebrated theorem of N. Wiener gives more by asserting that the ...
Page 2069
If the operator A in Ap has an inverse in B ( HP ) then , by Corollary 9.6 , A - 1 is in AP and the determinant S = det ( a ; ) has an inverse in A. Since A , contains all inverses , 8 - 1 is in A .. It follows from the definition of ...
If the operator A in Ap has an inverse in B ( HP ) then , by Corollary 9.6 , A - 1 is in AP and the determinant S = det ( a ; ) has an inverse in A. Since A , contains all inverses , 8 - 1 is in A .. It follows from the definition of ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 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 contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear 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 |