Linear Operators: Spectral theory |
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Page 929
... subspace which is neither { 0 } nor X for which we have TMCM , then M is called a ( non - trivial ) invariant subspace of X with respect to T. If X is a Hilbert space and if both M and its ortho- complement XM are invariant subspaces of ...
... subspace which is neither { 0 } nor X for which we have TMCM , then M is called a ( non - trivial ) invariant subspace of X with respect to T. If X is a Hilbert space and if both M and its ortho- complement XM are invariant subspaces of ...
Page 930
... subspaces for a given operator . It is not known whether every operator , distinct from the zero and identity operators , has a non - trivial invariant subspace . It is readily seen from Theorem VII.3.10 that if T is a bounded linear ...
... subspaces for a given operator . It is not known whether every operator , distinct from the zero and identity operators , has a non - trivial invariant subspace . It is readily seen from Theorem VII.3.10 that if T is a bounded linear ...
Page 1228
... subspace of D ( T * ) in- 1n ( D , OD_ ) . Clearly , 1 is closed and S 1 symmetric , and S 2 D ( T ) → S1 . If a e ... subspace of DD_ , and S = D ( T ) ℗ S1 . ( a ) The space is symmetric if and only if 1 is the graph of an isometric ...
... subspace of D ( T * ) in- 1n ( D , OD_ ) . Clearly , 1 is closed and S 1 symmetric , and S 2 D ( T ) → S1 . If a e ... subspace of DD_ , and S = D ( T ) ℗ S1 . ( a ) The space is symmetric if and only if 1 is the graph of an isometric ...
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BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero