Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |
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Page 2256
Suppose now that U is any neighborhood of zero in o ( R ) . Then , as observed in
the preceding paragraph , every point p in o ( R ) – U is contained in an open and
closed subset op of o ( R ) not containing zero . A finite collection Op1 , . . .
Suppose now that U is any neighborhood of zero in o ( R ) . Then , as observed in
the preceding paragraph , every point p in o ( R ) – U is contained in an open and
closed subset op of o ( R ) not containing zero . A finite collection Op1 , . . .
Page 2325
0 5 Rz < 211 onto the w - plane with zero removed . Since sin z ... In order to
obtain information on the zeros of M ( u ) from this , we now use Lemma 3 . We
know ... R ( 1 ) and R ( 2 ) , each of which contains exactly one zero of sin ( 2 — «
) = .
0 5 Rz < 211 onto the w - plane with zero removed . Since sin z ... In order to
obtain information on the zeros of M ( u ) from this , we now use Lemma 3 . We
know ... R ( 1 ) and R ( 2 ) , each of which contains exactly one zero of sin ( 2 — «
) = .
Page 2462
Moreover , if C belongs to the trace class C1 , then T , C converges to zero in
trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( {
xe H | 1 } ) is conditionally compact , and thus for each € > 0 there exists a finite
set ...
Moreover , if C belongs to the trace class C1 , then T , C converges to zero in
trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( {
xe H | 1 } ) is conditionally compact , and thus for each € > 0 there exists a finite
set ...
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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 |