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 |
From inside the book
Results 1-3 of 58
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 * ) * = e * *
e ...
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 * ) * = e * *
e ...
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 inverse a - 1 is
in ...
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 inverse a - 1 is
in ...
Page 2069
Let the operator a in U have an inverse in B ( H ) . If a is of ... Let A , be a
subalgebra of A which contains all inverses . ... 6 , A - 1 is in AP and the
determinant 8 = det ( ay ) has an inverse in A . Since A , contains all inverses , 8 -
1 is in A . .
Let the operator a in U have an inverse in B ( H ) . If a is of ... Let A , be a
subalgebra of A which contains all inverses . ... 6 , A - 1 is in AP and the
determinant 8 = det ( ay ) has an inverse in A . Since A , contains all inverses , 8 -
1 is in A . .
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
SPECTRAL OPERATORS XV Spectral Operators | 1924 |
Introduction | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
32 other sections not shown
Other editions - View all
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 |