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 2070
Theorem 1 shows that the operator a determines a and f uniquely , and so we
may define a norm in A , by the equation ( 18 ) lalo = 10 + 1flo , ae A . . It is clear
that A , is a B - space under this norm . It is also an algebra , for the product of two
...
Theorem 1 shows that the operator a determines a and f uniquely , and so we
may define a norm in A , by the equation ( 18 ) lalo = 10 + 1flo , ae A . . It is clear
that A , is a B - space under this norm . It is also an algebra , for the product of two
...
Page 2450
It follows that { Anx } is a Cauchy sequence of vectors for each x € X . Moreover ,
by definition of the norm in A , { RAnx } is also a Cauchy sequence . If A = limno .
An , then , since R is a closed operator , we have Ax e D ( R ) for each x e X , and
...
It follows that { Anx } is a Cauchy sequence of vectors for each x € X . Moreover ,
by definition of the norm in A , { RAnx } is also a Cauchy sequence . If A = limno .
An , then , since R is a closed operator , we have Ax e D ( R ) for each x e X , and
...
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 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 |