Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |
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Page 1994
Let any converge for each o in H . Theorem 4 shows that 12on1 = no , and
Theorem II . 3 . 6 proves ... Then , by Theorem 4 , ang = F - nx , and since and
converges , we see from the continuity of F that liml1n ( s ) – Am ( s ) / 2 ds = 0 , m
. + 00vo ...
Let any converge for each o in H . Theorem 4 shows that 12on1 = no , and
Theorem II . 3 . 6 proves ... Then , by Theorem 4 , ang = F - nx , and since and
converges , we see from the continuity of F that liml1n ( s ) – Am ( s ) / 2 ds = 0 , m
. + 00vo ...
Page 2218
It must be shown that { Eq } converges strongly to E . By Lemma 6 , E is in B and
so a consideration of the sequence { Ea – E } shows that it may be assumed that
E = 0 . Thus , to make an indirect proof , it is assumed that the sequence { Ea } is ...
It must be shown that { Eq } converges strongly to E . By Lemma 6 , E is in B and
so a consideration of the sequence { Ea – E } shows that it may be assumed that
E = 0 . Thus , to make an indirect proof , it is assumed that the sequence { Ea } is ...
Page 2462
Moreover , if C belongs to the trace class C1 , then TnC converges to zero in
trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( {
XE H | | 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there exists a
finite ...
Moreover , if C belongs to the trace class C1 , then TnC converges to zero in
trace norm , and CT * converges to zero in trace norm . PROOF . The set K = C ( {
XE H | | 2 < 1 } ) is conditionally compact , and thus for each ε > 0 there exists a
finite ...
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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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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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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: 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 |