Linear Operators: Spectral theory |
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Page 929
Invariant subspaces . If T is an operator in a B - space X , and if M is a closed linear subspace which is neither { 0 } nor X for which we have TM C M , then M is called a ( non - trivial ) invariant subspace of X with respect to T. If ...
Invariant subspaces . If T is an operator in a B - space X , and if M is a closed linear subspace which is neither { 0 } nor X for which we have TM C M , then M is called a ( non - trivial ) invariant subspace of X with respect to T. If ...
Page 930
this is far from clear , and it is of considerable interest to find non - triv . ial invariant subspaces for a ... Aronszajn and Smith [ 1 ] have shown that every compact operator has an invariant subspace even when o ( T ) { 0 } .
this is far from clear , and it is of considerable interest to find non - triv . ial invariant subspaces for a ... Aronszajn and Smith [ 1 ] have shown that every compact operator has an invariant subspace even when o ( T ) { 0 } .
Page 1228
There is a one - to - one correspondence between closed symmetric subspaces S of the Hilbert space D ( T * ) which contain D ... Conversely , if S is a closed symmetric subspace of D ( T * ) including D ( T ) , put Si = SO ( D.D_ ) .
There is a one - to - one correspondence between closed symmetric subspaces S of the Hilbert space D ( T * ) which contain D ... Conversely , if S is a closed symmetric subspace of D ( T * ) including D ( T ) , put Si = SO ( D.D_ ) .
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Contents
8 | 876 |
859 | 885 |
extensive presentation of applications of the spectral theorem | 911 |
Copyright | |
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additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero