Linear Operators: Spectral theory |
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Page 929
... invariant subspaces of X with respect to T , then M is said to reduce T. It is not difficult to see that a non - trivial subspace of Hilbert space may be an invariant subspace for an opera- tor but not reduce the operator . In fact , an ...
... invariant subspaces of X with respect to T , then M is said to reduce T. It is not difficult to see that a non - trivial subspace of Hilbert space may be an invariant subspace for an opera- tor but not reduce the operator . In fact , an ...
Page 930
... invariant 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 ...
... invariant 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 ...
Page 1911
... Invariant measures , V.11.22 ( 460 ) , VI.9.38-44 ( 516 ) Invariant metric , in a group , ( 90–91 ) in a linear space , iI.1.10 ( 51 ) Invariant set , ( 3 ) Invariant subgroup , ( 35 ) Invariant subspace , definition of , X.9 ( 929 ) ...
... Invariant measures , V.11.22 ( 460 ) , VI.9.38-44 ( 516 ) Invariant metric , in a group , ( 90–91 ) in a linear space , iI.1.10 ( 51 ) Invariant set , ( 3 ) Invariant subgroup , ( 35 ) Invariant subspace , definition of , X.9 ( 929 ) ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero